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

Percentage Accurate: 99.9% → 100.0%

Time: 5.1s

Alternatives: 11

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 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 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 100.0%

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

   3. distribute-rgt-in 97.6%

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

   4. associate-+l+ 97.6%

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

   5. +-commutative 97.6%

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

   6. count-2 97.6%

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

   7. distribute-rgt-in 100.0%

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

   8. *-commutative 100.0%

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

   9. fma-def 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

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 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 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. Final simplification 100.0%

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

Alternative 3: 58.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-218}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-200}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -9e-9)
     t_2
     (if (<= y -1.95e-73)
       t_1
       (if (<= y -1.65e-107)
         t_2
         (if (<= y -2.4e-218)
           (* x t)
           (if (<= y 1.15e-262)
             t_1
             (if (<= y 1.75e-200) (* x t) (if (<= y 8.2e-51) t_1 t_2)))))))))

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 * 2.0));
	double tmp;
	if (y <= -9e-9) {
		tmp = t_2;
	} else if (y <= -1.95e-73) {
		tmp = t_1;
	} else if (y <= -1.65e-107) {
		tmp = t_2;
	} else if (y <= -2.4e-218) {
		tmp = x * t;
	} else if (y <= 1.15e-262) {
		tmp = t_1;
	} else if (y <= 1.75e-200) {
		tmp = x * t;
	} else if (y <= 8.2e-51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 * 2.0d0))
    if (y <= (-9d-9)) then
        tmp = t_2
    else if (y <= (-1.95d-73)) then
        tmp = t_1
    else if (y <= (-1.65d-107)) then
        tmp = t_2
    else if (y <= (-2.4d-218)) then
        tmp = x * t
    else if (y <= 1.15d-262) then
        tmp = t_1
    else if (y <= 1.75d-200) then
        tmp = x * t
    else if (y <= 8.2d-51) then
        tmp = t_1
    else
        tmp = t_2
    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 * 2.0));
	double tmp;
	if (y <= -9e-9) {
		tmp = t_2;
	} else if (y <= -1.95e-73) {
		tmp = t_1;
	} else if (y <= -1.65e-107) {
		tmp = t_2;
	} else if (y <= -2.4e-218) {
		tmp = x * t;
	} else if (y <= 1.15e-262) {
		tmp = t_1;
	} else if (y <= 1.75e-200) {
		tmp = x * t;
	} else if (y <= 8.2e-51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -9e-9:
		tmp = t_2
	elif y <= -1.95e-73:
		tmp = t_1
	elif y <= -1.65e-107:
		tmp = t_2
	elif y <= -2.4e-218:
		tmp = x * t
	elif y <= 1.15e-262:
		tmp = t_1
	elif y <= 1.75e-200:
		tmp = x * t
	elif y <= 8.2e-51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -9e-9)
		tmp = t_2;
	elseif (y <= -1.95e-73)
		tmp = t_1;
	elseif (y <= -1.65e-107)
		tmp = t_2;
	elseif (y <= -2.4e-218)
		tmp = Float64(x * t);
	elseif (y <= 1.15e-262)
		tmp = t_1;
	elseif (y <= 1.75e-200)
		tmp = Float64(x * t);
	elseif (y <= 8.2e-51)
		tmp = t_1;
	else
		tmp = t_2;
	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 * 2.0));
	tmp = 0.0;
	if (y <= -9e-9)
		tmp = t_2;
	elseif (y <= -1.95e-73)
		tmp = t_1;
	elseif (y <= -1.65e-107)
		tmp = t_2;
	elseif (y <= -2.4e-218)
		tmp = x * t;
	elseif (y <= 1.15e-262)
		tmp = t_1;
	elseif (y <= 1.75e-200)
		tmp = x * t;
	elseif (y <= 8.2e-51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-9], t$95$2, If[LessEqual[y, -1.95e-73], t$95$1, If[LessEqual[y, -1.65e-107], t$95$2, If[LessEqual[y, -2.4e-218], N[(x * t), $MachinePrecision], If[LessEqual[y, 1.15e-262], t$95$1, If[LessEqual[y, 1.75e-200], N[(x * t), $MachinePrecision], If[LessEqual[y, 8.2e-51], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999953e-9 or -1.94999999999999991e-73 < y < -1.65000000000000002e-107 or 8.19999999999999947e-51 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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 73.2%

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

   if -8.99999999999999953e-9 < y < -1.94999999999999991e-73 or -2.4000000000000001e-218 < y < 1.15000000000000005e-262 or 1.75000000000000011e-200 < y < 8.19999999999999947e-51

   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 59.1%

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

   if -1.65000000000000002e-107 < y < -2.4000000000000001e-218 or 1.15000000000000005e-262 < y < 1.75000000000000011e-200

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 68.7%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-73}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-107}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-218}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-262}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-200}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 4: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-107} \lor \neg \left(y \leq 2.8 \cdot 10^{+69}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.1e-107) (not (<= y 2.8e+69)))
   (+ (* 2.0 (* x (+ y z))) (* y 5.0))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.1e-107) || !(y <= 2.8e+69)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} 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 <= (-4.1d-107)) .or. (.not. (y <= 2.8d+69))) then
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    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 <= -4.1e-107) || !(y <= 2.8e+69)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.1e-107) or not (y <= 2.8e+69):
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.1e-107) || !(y <= 2.8e+69))
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	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 <= -4.1e-107) || ~((y <= 2.8e+69)))
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.1e-107], N[Not[LessEqual[y, 2.8e+69]], $MachinePrecision]], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0999999999999999e-107 or 2.79999999999999982e69 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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 t around 0 90.8%

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

   if -4.0999999999999999e-107 < y < 2.79999999999999982e69

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-107} \lor \neg \left(y \leq 2.8 \cdot 10^{+69}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 5: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+46} \lor \neg \left(z \leq 1.4 \cdot 10^{+23}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5e+46) (not (<= z 1.4e+23)))
   (+ (* 2.0 (* x (+ y z))) (* y 5.0))
   (+ (* y 5.0) (* x (+ t (* y 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e+46) || !(z <= 1.4e+23)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5d+46)) .or. (.not. (z <= 1.4d+23))) then
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    else
        tmp = (y * 5.0d0) + (x * (t + (y * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e+46) || !(z <= 1.4e+23)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5e+46) or not (z <= 1.4e+23):
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = (y * 5.0) + (x * (t + (y * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5e+46) || !(z <= 1.4e+23))
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5e+46) || ~((z <= 1.4e+23)))
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	else
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5e+46], N[Not[LessEqual[z, 1.4e+23]], $MachinePrecision]], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e46 or 1.4e23 < z

   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 t around 0 88.9%

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

   if -5.0000000000000002e46 < z < 1.4e23

   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 z around 0 94.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+46} \lor \neg \left(z \leq 1.4 \cdot 10^{+23}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]

Alternative 6: 44.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+168}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-270}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+121}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= t -7.4e+168)
     (* x t)
     (if (<= t -4e-275)
       t_1
       (if (<= t 1.25e-270)
         (* y 5.0)
         (if (<= t 2.9e-185) t_1 (if (<= t 3.7e+121) (* y 5.0) (* x t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (t <= -7.4e+168) {
		tmp = x * t;
	} else if (t <= -4e-275) {
		tmp = t_1;
	} else if (t <= 1.25e-270) {
		tmp = y * 5.0;
	} else if (t <= 2.9e-185) {
		tmp = t_1;
	} else if (t <= 3.7e+121) {
		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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (t <= (-7.4d+168)) then
        tmp = x * t
    else if (t <= (-4d-275)) then
        tmp = t_1
    else if (t <= 1.25d-270) then
        tmp = y * 5.0d0
    else if (t <= 2.9d-185) then
        tmp = t_1
    else if (t <= 3.7d+121) 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 t_1 = 2.0 * (x * z);
	double tmp;
	if (t <= -7.4e+168) {
		tmp = x * t;
	} else if (t <= -4e-275) {
		tmp = t_1;
	} else if (t <= 1.25e-270) {
		tmp = y * 5.0;
	} else if (t <= 2.9e-185) {
		tmp = t_1;
	} else if (t <= 3.7e+121) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if t <= -7.4e+168:
		tmp = x * t
	elif t <= -4e-275:
		tmp = t_1
	elif t <= 1.25e-270:
		tmp = y * 5.0
	elif t <= 2.9e-185:
		tmp = t_1
	elif t <= 3.7e+121:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (t <= -7.4e+168)
		tmp = Float64(x * t);
	elseif (t <= -4e-275)
		tmp = t_1;
	elseif (t <= 1.25e-270)
		tmp = Float64(y * 5.0);
	elseif (t <= 2.9e-185)
		tmp = t_1;
	elseif (t <= 3.7e+121)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (t <= -7.4e+168)
		tmp = x * t;
	elseif (t <= -4e-275)
		tmp = t_1;
	elseif (t <= 1.25e-270)
		tmp = y * 5.0;
	elseif (t <= 2.9e-185)
		tmp = t_1;
	elseif (t <= 3.7e+121)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e+168], N[(x * t), $MachinePrecision], If[LessEqual[t, -4e-275], t$95$1, If[LessEqual[t, 1.25e-270], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 2.9e-185], t$95$1, If[LessEqual[t, 3.7e+121], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.40000000000000018e168 or 3.70000000000000013e121 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 71.1%

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

   if -7.40000000000000018e168 < t < -3.99999999999999974e-275 or 1.2499999999999999e-270 < t < 2.89999999999999995e-185

   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 z around inf 51.1%

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

   if -3.99999999999999974e-275 < t < 1.2499999999999999e-270 or 2.89999999999999995e-185 < t < 3.70000000000000013e121

   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 49.3%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+168}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-275}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-270}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-185}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+121}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 7: 77.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -8.8e+123)
     t_1
     (if (<= y -5.3e-107)
       (+ (* y 5.0) (* 2.0 (* x z)))
       (if (<= y 1.2e+104) (* x (+ t (* z 2.0))) 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 <= -8.8e+123) {
		tmp = t_1;
	} else if (y <= -5.3e-107) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else if (y <= 1.2e+104) {
		tmp = x * (t + (z * 2.0));
	} 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 <= (-8.8d+123)) then
        tmp = t_1
    else if (y <= (-5.3d-107)) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    else if (y <= 1.2d+104) then
        tmp = x * (t + (z * 2.0d0))
    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 <= -8.8e+123) {
		tmp = t_1;
	} else if (y <= -5.3e-107) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else if (y <= 1.2e+104) {
		tmp = x * (t + (z * 2.0));
	} 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 <= -8.8e+123:
		tmp = t_1
	elif y <= -5.3e-107:
		tmp = (y * 5.0) + (2.0 * (x * z))
	elif y <= 1.2e+104:
		tmp = x * (t + (z * 2.0))
	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 <= -8.8e+123)
		tmp = t_1;
	elseif (y <= -5.3e-107)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	elseif (y <= 1.2e+104)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	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 <= -8.8e+123)
		tmp = t_1;
	elseif (y <= -5.3e-107)
		tmp = (y * 5.0) + (2.0 * (x * z));
	elseif (y <= 1.2e+104)
		tmp = x * (t + (z * 2.0));
	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, -8.8e+123], t$95$1, If[LessEqual[y, -5.3e-107], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+104], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.79999999999999969e123 or 1.2e104 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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 88.9%

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

   if -8.79999999999999969e123 < y < -5.3e-107

   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 t around 0 88.7%

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

   5. Taylor expanded in y around 0 88.5%

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

   if -5.3e-107 < y < 1.2e104

   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 81.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 8: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (t + ((y + z) * 2.0d0))) + (y * 5.0d0)
end function

Java

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

Python

def code(x, y, z, t):
	return (x * (t + ((y + z) * 2.0))) + (y * 5.0)

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (t + ((y + z) * 2.0))) + (y * 5.0);
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. count-2 99.9%

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

   4. *-commutative 99.9%

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

3. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

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

Alternative 9: 78.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-5} \lor \neg \left(y \leq 1.9 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.06e-5) (not (<= y 1.9e+102)))
   (* 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 <= -1.06e-5) || !(y <= 1.9e+102)) {
		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 <= (-1.06d-5)) .or. (.not. (y <= 1.9d+102))) 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 <= -1.06e-5) || !(y <= 1.9e+102)) {
		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 <= -1.06e-5) or not (y <= 1.9e+102):
		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 <= -1.06e-5) || !(y <= 1.9e+102))
		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 <= -1.06e-5) || ~((y <= 1.9e+102)))
		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, -1.06e-5], N[Not[LessEqual[y, 1.9e+102]], $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 < -1.06e-5 or 1.89999999999999989e102 < y

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. 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 84.7%

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

   if -1.06e-5 < y < 1.89999999999999989e102

   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 79.3%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-5} \lor \neg \left(y \leq 1.9 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 10: 44.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+122}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.5e+49) (* x t) (if (<= t 5.2e+122) (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.5e+49) {
		tmp = x * t;
	} else if (t <= 5.2e+122) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-9.5d+49)) then
        tmp = x * t
    else if (t <= 5.2d+122) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.5e+49) {
		tmp = x * t;
	} else if (t <= 5.2e+122) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.5e+49:
		tmp = x * t
	elif t <= 5.2e+122:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.5e+49)
		tmp = Float64(x * t);
	elseif (t <= 5.2e+122)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9.5e+49)
		tmp = x * t;
	elseif (t <= 5.2e+122)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.5e+49], N[(x * t), $MachinePrecision], If[LessEqual[t, 5.2e+122], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.49999999999999969e49 or 5.20000000000000015e122 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 61.7%

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

   if -9.49999999999999969e49 < t < 5.20000000000000015e122

   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 36.0%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+122}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 11: 30.4% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 29.2%

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

3. Final simplification 29.2%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023199 
(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)))