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

Percentage Accurate: 99.9% → 100.0%

Time: 5.4s

Alternatives: 10

Speedup: 1.0×

• 26.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% 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 98.9%

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

   1. +-commutative 98.9%

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

   2. fma-def 99.3%

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

   3. distribute-rgt-in 96.5%

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

   4. associate-+l+ 96.5%

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

   5. +-commutative 96.5%

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

   6. count-2 96.5%

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

   7. distribute-rgt-in 99.3%

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

   8. *-commutative 99.3%

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

   9. fma-def 99.3%

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

3. Applied egg-rr 99.3%

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

4. Final simplification 99.3%

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

Alternative 2: 99.9% 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 98.9%

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

   1. fma-def 98.9%

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

   2. associate-+l+ 98.9%

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

   3. +-commutative 98.9%

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

   4. count-2 98.9%

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

3. Simplified 98.9%

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

4. Final simplification 98.9%

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

Alternative 3: 43.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-209}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-270}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 10^{-247}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= z -2.6e+103)
     t_1
     (if (<= z -6.5e-5)
       (* x t)
       (if (<= z -2e-209)
         (* y 5.0)
         (if (<= z -1.16e-270)
           (* x t)
           (if (<= z 1e-247)
             (* y (* x 2.0))
             (if (<= z 4.5e+51) (* x t) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (z <= -2.6e+103) {
		tmp = t_1;
	} else if (z <= -6.5e-5) {
		tmp = x * t;
	} else if (z <= -2e-209) {
		tmp = y * 5.0;
	} else if (z <= -1.16e-270) {
		tmp = x * t;
	} else if (z <= 1e-247) {
		tmp = y * (x * 2.0);
	} else if (z <= 4.5e+51) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (z <= (-2.6d+103)) then
        tmp = t_1
    else if (z <= (-6.5d-5)) then
        tmp = x * t
    else if (z <= (-2d-209)) then
        tmp = y * 5.0d0
    else if (z <= (-1.16d-270)) then
        tmp = x * t
    else if (z <= 1d-247) then
        tmp = y * (x * 2.0d0)
    else if (z <= 4.5d+51) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (z <= -2.6e+103) {
		tmp = t_1;
	} else if (z <= -6.5e-5) {
		tmp = x * t;
	} else if (z <= -2e-209) {
		tmp = y * 5.0;
	} else if (z <= -1.16e-270) {
		tmp = x * t;
	} else if (z <= 1e-247) {
		tmp = y * (x * 2.0);
	} else if (z <= 4.5e+51) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if z <= -2.6e+103:
		tmp = t_1
	elif z <= -6.5e-5:
		tmp = x * t
	elif z <= -2e-209:
		tmp = y * 5.0
	elif z <= -1.16e-270:
		tmp = x * t
	elif z <= 1e-247:
		tmp = y * (x * 2.0)
	elif z <= 4.5e+51:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.6e+103)
		tmp = t_1;
	elseif (z <= -6.5e-5)
		tmp = Float64(x * t);
	elseif (z <= -2e-209)
		tmp = Float64(y * 5.0);
	elseif (z <= -1.16e-270)
		tmp = Float64(x * t);
	elseif (z <= 1e-247)
		tmp = Float64(y * Float64(x * 2.0));
	elseif (z <= 4.5e+51)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.6e+103)
		tmp = t_1;
	elseif (z <= -6.5e-5)
		tmp = x * t;
	elseif (z <= -2e-209)
		tmp = y * 5.0;
	elseif (z <= -1.16e-270)
		tmp = x * t;
	elseif (z <= 1e-247)
		tmp = y * (x * 2.0);
	elseif (z <= 4.5e+51)
		tmp = x * t;
	else
		tmp = t_1;
	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[z, -2.6e+103], t$95$1, If[LessEqual[z, -6.5e-5], N[(x * t), $MachinePrecision], If[LessEqual[z, -2e-209], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, -1.16e-270], N[(x * t), $MachinePrecision], If[LessEqual[z, 1e-247], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+51], N[(x * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6000000000000002e103 or 4.5e51 < z

   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 z around inf 84.6%

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

   3. Taylor expanded in z around inf 68.5%

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

   if -2.6000000000000002e103 < z < -6.49999999999999943e-5 or -2.0000000000000001e-209 < z < -1.16000000000000006e-270 or 1e-247 < z < 4.5e51

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 77.0%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   3. Step-by-step derivation

      1. +-commutative 77.0%

         \[\leadsto \color{blue}{y \cdot 5 + t \cdot x} \]

      2. fma-def 77.0%

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

      3. *-commutative 77.0%

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

   4. Applied egg-rr 77.0%

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

   5. Taylor expanded in y around 0 55.8%

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

      1. *-commutative 55.8%

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

   7. Simplified 55.8%

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

   if -6.49999999999999943e-5 < z < -2.0000000000000001e-209

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 43.2%

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

   4. Simplified 43.2%

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

   if -1.16000000000000006e-270 < z < 1e-247

   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 y around inf 73.7%

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

      1. *-commutative 73.7%

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

      2. distribute-rgt-in 73.7%

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

      3. *-commutative 73.7%

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

      4. *-commutative 73.7%

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

   6. Applied egg-rr 73.7%

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

   7. Taylor expanded in x around inf 48.8%

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

      1. associate-*r* 48.8%

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

      2. *-commutative 48.8%

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

      3. associate-*r* 48.8%

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

   9. Simplified 48.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+103}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-209}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-270}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 10^{-247}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+183}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (+ (* y 5.0) (* x t))))
   (if (<= z -8.2e+108)
     t_1
     (if (<= z -4.2e-35)
       t_2
       (if (<= z 4.6e-248)
         (* y (+ 5.0 (* x 2.0)))
         (if (<= z 3e+183) t_2 t_1))))))

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 * t);
	double tmp;
	if (z <= -8.2e+108) {
		tmp = t_1;
	} else if (z <= -4.2e-35) {
		tmp = t_2;
	} else if (z <= 4.6e-248) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (z <= 3e+183) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    t_2 = (y * 5.0d0) + (x * t)
    if (z <= (-8.2d+108)) then
        tmp = t_1
    else if (z <= (-4.2d-35)) then
        tmp = t_2
    else if (z <= 4.6d-248) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else if (z <= 3d+183) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = (y * 5.0) + (x * t);
	double tmp;
	if (z <= -8.2e+108) {
		tmp = t_1;
	} else if (z <= -4.2e-35) {
		tmp = t_2;
	} else if (z <= 4.6e-248) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (z <= 3e+183) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = (y * 5.0) + (x * t)
	tmp = 0
	if z <= -8.2e+108:
		tmp = t_1
	elif z <= -4.2e-35:
		tmp = t_2
	elif z <= 4.6e-248:
		tmp = y * (5.0 + (x * 2.0))
	elif z <= 3e+183:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(Float64(y * 5.0) + Float64(x * t))
	tmp = 0.0
	if (z <= -8.2e+108)
		tmp = t_1;
	elseif (z <= -4.2e-35)
		tmp = t_2;
	elseif (z <= 4.6e-248)
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	elseif (z <= 3e+183)
		tmp = t_2;
	else
		tmp = t_1;
	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 * t);
	tmp = 0.0;
	if (z <= -8.2e+108)
		tmp = t_1;
	elseif (z <= -4.2e-35)
		tmp = t_2;
	elseif (z <= 4.6e-248)
		tmp = y * (5.0 + (x * 2.0));
	elseif (z <= 3e+183)
		tmp = t_2;
	else
		tmp = t_1;
	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[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+108], t$95$1, If[LessEqual[z, -4.2e-35], t$95$2, If[LessEqual[z, 4.6e-248], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+183], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.1999999999999998e108 or 2.99999999999999996e183 < z

   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 z around inf 88.9%

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

   3. Taylor expanded in z around inf 77.5%

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

   if -8.1999999999999998e108 < z < -4.2e-35 or 4.6e-248 < z < 2.99999999999999996e183

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 73.6%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]

   if -4.2e-35 < z < 4.6e-248

   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 y around inf 71.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+108}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-35}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+183}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 5: 99.9% 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 98.9%

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

2. Final simplification 98.9%

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

Alternative 6: 44.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-209}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+48}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= z -3.7e+103)
     t_1
     (if (<= z -7.2e-6)
       (* x t)
       (if (<= z -2.4e-209) (* y 5.0) (if (<= z 2.4e+48) (* x t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (z <= -3.7e+103) {
		tmp = t_1;
	} else if (z <= -7.2e-6) {
		tmp = x * t;
	} else if (z <= -2.4e-209) {
		tmp = y * 5.0;
	} else if (z <= 2.4e+48) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (z <= (-3.7d+103)) then
        tmp = t_1
    else if (z <= (-7.2d-6)) then
        tmp = x * t
    else if (z <= (-2.4d-209)) then
        tmp = y * 5.0d0
    else if (z <= 2.4d+48) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (z <= -3.7e+103) {
		tmp = t_1;
	} else if (z <= -7.2e-6) {
		tmp = x * t;
	} else if (z <= -2.4e-209) {
		tmp = y * 5.0;
	} else if (z <= 2.4e+48) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if z <= -3.7e+103:
		tmp = t_1
	elif z <= -7.2e-6:
		tmp = x * t
	elif z <= -2.4e-209:
		tmp = y * 5.0
	elif z <= 2.4e+48:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -3.7e+103)
		tmp = t_1;
	elseif (z <= -7.2e-6)
		tmp = Float64(x * t);
	elseif (z <= -2.4e-209)
		tmp = Float64(y * 5.0);
	elseif (z <= 2.4e+48)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (z <= -3.7e+103)
		tmp = t_1;
	elseif (z <= -7.2e-6)
		tmp = x * t;
	elseif (z <= -2.4e-209)
		tmp = y * 5.0;
	elseif (z <= 2.4e+48)
		tmp = x * t;
	else
		tmp = t_1;
	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[z, -3.7e+103], t$95$1, If[LessEqual[z, -7.2e-6], N[(x * t), $MachinePrecision], If[LessEqual[z, -2.4e-209], N[(y * 5.0), $MachinePrecision], If[LessEqual[z, 2.4e+48], N[(x * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.70000000000000033e103 or 2.4000000000000001e48 < z

   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 z around inf 84.6%

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

   3. Taylor expanded in z around inf 68.5%

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

   if -3.70000000000000033e103 < z < -7.19999999999999967e-6 or -2.4000000000000001e-209 < z < 2.4000000000000001e48

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 72.1%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   3. Step-by-step derivation

      1. +-commutative 72.1%

         \[\leadsto \color{blue}{y \cdot 5 + t \cdot x} \]

      2. fma-def 72.1%

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

      3. *-commutative 72.1%

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

   4. Applied egg-rr 72.1%

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

   5. Taylor expanded in y around 0 50.7%

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

      1. *-commutative 50.7%

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

   7. Simplified 50.7%

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

   if -7.19999999999999967e-6 < z < -2.4000000000000001e-209

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 43.2%

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

   4. Simplified 43.2%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+103}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-209}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+48}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 7: 57.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-284}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-110}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.7e+73)
     t_1
     (if (<= y 1.1e-284) (* x t) (if (<= y 1.65e-110) (* 2.0 (* x z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.7e+73) {
		tmp = t_1;
	} else if (y <= 1.1e-284) {
		tmp = x * t;
	} else if (y <= 1.65e-110) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.7d+73)) then
        tmp = t_1
    else if (y <= 1.1d-284) then
        tmp = x * t
    else if (y <= 1.65d-110) then
        tmp = 2.0d0 * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.7e+73) {
		tmp = t_1;
	} else if (y <= 1.1e-284) {
		tmp = x * t;
	} else if (y <= 1.65e-110) {
		tmp = 2.0 * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.7e+73:
		tmp = t_1
	elif y <= 1.1e-284:
		tmp = x * t
	elif y <= 1.65e-110:
		tmp = 2.0 * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.7e+73)
		tmp = t_1;
	elseif (y <= 1.1e-284)
		tmp = Float64(x * t);
	elseif (y <= 1.65e-110)
		tmp = Float64(2.0 * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.7e+73)
		tmp = t_1;
	elseif (y <= 1.1e-284)
		tmp = x * t;
	elseif (y <= 1.65e-110)
		tmp = 2.0 * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+73], t$95$1, If[LessEqual[y, 1.1e-284], N[(x * t), $MachinePrecision], If[LessEqual[y, 1.65e-110], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7000000000000001e73 or 1.65e-110 < y

   1. Initial program 98.4%

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

      1. fma-def 98.4%

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

      2. associate-+l+ 98.4%

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

      3. +-commutative 98.4%

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

      4. count-2 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 74.9%

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

   if -1.7000000000000001e73 < y < 1.1e-284

   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 66.4%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   3. Step-by-step derivation

      1. +-commutative 66.4%

         \[\leadsto \color{blue}{y \cdot 5 + t \cdot x} \]

      2. fma-def 66.4%

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

      3. *-commutative 66.4%

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

   4. Applied egg-rr 66.4%

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

   5. Taylor expanded in y around 0 59.9%

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

      1. *-commutative 59.9%

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

   7. Simplified 59.9%

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

   if 1.1e-284 < y < 1.65e-110

   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 60.6%

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

   3. Taylor expanded in z around inf 50.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-284}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-110}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 8: 88.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-45} \lor \neg \left(x \leq 2.05 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9e-45) (not (<= x 2.05e-10)))
   (* 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 <= -9e-45) || !(x <= 2.05e-10)) {
		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 <= (-9d-45)) .or. (.not. (x <= 2.05d-10))) 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 <= -9e-45) || !(x <= 2.05e-10)) {
		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 <= -9e-45) or not (x <= 2.05e-10):
		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 <= -9e-45) || !(x <= 2.05e-10))
		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 <= -9e-45) || ~((x <= 2.05e-10)))
		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, -9e-45], N[Not[LessEqual[x, 2.05e-10]], $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 < -8.9999999999999997e-45 or 2.0499999999999999e-10 < x

   1. Initial program 98.8%

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

      1. fma-def 98.8%

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

      2. associate-+l+ 98.8%

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

      3. +-commutative 98.8%

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

      4. count-2 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 97.2%

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

   if -8.9999999999999997e-45 < x < 2.0499999999999999e-10

   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 t around inf 81.7%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-45} \lor \neg \left(x \leq 2.05 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 9: 46.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-95}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 17000:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.1e-95) (* x t) (if (<= x 17000.0) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.1e-95) {
		tmp = x * t;
	} else if (x <= 17000.0) {
		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 <= (-1.1d-95)) then
        tmp = x * t
    else if (x <= 17000.0d0) 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 <= -1.1e-95) {
		tmp = x * t;
	} else if (x <= 17000.0) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.1e-95:
		tmp = x * t
	elif x <= 17000.0:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.1e-95)
		tmp = Float64(x * t);
	elseif (x <= 17000.0)
		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 <= -1.1e-95)
		tmp = x * t;
	elseif (x <= 17000.0)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.1e-95], N[(x * t), $MachinePrecision], If[LessEqual[x, 17000.0], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0999999999999999e-95 or 17000 < x

   1. Initial program 99.4%

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

   2. Taylor expanded in t around inf 43.4%

      \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
   3. Step-by-step derivation

      1. +-commutative 43.4%

         \[\leadsto \color{blue}{y \cdot 5 + t \cdot x} \]

      2. fma-def 43.4%

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

      3. *-commutative 43.4%

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

   4. Applied egg-rr 43.4%

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

   5. Taylor expanded in y around 0 40.5%

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

      1. *-commutative 40.5%

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

   7. Simplified 40.5%

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

   if -1.0999999999999999e-95 < x < 17000

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 58.2%

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

   4. Simplified 58.2%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-95}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 17000:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 10: 30.5% 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 98.9%

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

2. Taylor expanded in t around inf 56.0%

   \[\leadsto \color{blue}{t \cdot x} + y \cdot 5 \]
3. Step-by-step derivation

   1. +-commutative 56.0%

      \[\leadsto \color{blue}{y \cdot 5 + t \cdot x} \]

   2. fma-def 56.0%

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

   3. *-commutative 56.0%

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

4. Applied egg-rr 56.0%

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

5. Taylor expanded in y around 0 33.8%

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

   1. *-commutative 33.8%

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

7. Simplified 33.8%

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

8. Final simplification 33.8%

   \[\leadsto x \cdot t \]

Reproduce

herbie shell --seed 2023196 
(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)))