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

Percentage Accurate: 99.8% → 100.0%

Time: 8.9s

Alternatives: 14

Speedup: 1.0×

• 27.0% 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: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 100.0%

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

   3. associate-+l+ 100.0%

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

   4. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

   5. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

   6. *-un-lft-identity 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

   7. distribute-rgt-out 100.0%

      \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

   8. metadata-eval 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 45.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+23}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-49}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-211}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= t -3.4e+23)
     (* x t)
     (if (<= t -3.8e-49)
       (* y 5.0)
       (if (<= t -7.4e-121)
         t_1
         (if (<= t -1.35e-211)
           (* y 5.0)
           (if (<= t 5.5e-189)
             t_1
             (if (<= t 1.7e-55) (* y 5.0) (if (<= t 3e+55) t_1 (* x t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (t <= -3.4e+23) {
		tmp = x * t;
	} else if (t <= -3.8e-49) {
		tmp = y * 5.0;
	} else if (t <= -7.4e-121) {
		tmp = t_1;
	} else if (t <= -1.35e-211) {
		tmp = y * 5.0;
	} else if (t <= 5.5e-189) {
		tmp = t_1;
	} else if (t <= 1.7e-55) {
		tmp = y * 5.0;
	} else if (t <= 3e+55) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (t <= (-3.4d+23)) then
        tmp = x * t
    else if (t <= (-3.8d-49)) then
        tmp = y * 5.0d0
    else if (t <= (-7.4d-121)) then
        tmp = t_1
    else if (t <= (-1.35d-211)) then
        tmp = y * 5.0d0
    else if (t <= 5.5d-189) then
        tmp = t_1
    else if (t <= 1.7d-55) then
        tmp = y * 5.0d0
    else if (t <= 3d+55) then
        tmp = t_1
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (t <= -3.4e+23) {
		tmp = x * t;
	} else if (t <= -3.8e-49) {
		tmp = y * 5.0;
	} else if (t <= -7.4e-121) {
		tmp = t_1;
	} else if (t <= -1.35e-211) {
		tmp = y * 5.0;
	} else if (t <= 5.5e-189) {
		tmp = t_1;
	} else if (t <= 1.7e-55) {
		tmp = y * 5.0;
	} else if (t <= 3e+55) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if t <= -3.4e+23:
		tmp = x * t
	elif t <= -3.8e-49:
		tmp = y * 5.0
	elif t <= -7.4e-121:
		tmp = t_1
	elif t <= -1.35e-211:
		tmp = y * 5.0
	elif t <= 5.5e-189:
		tmp = t_1
	elif t <= 1.7e-55:
		tmp = y * 5.0
	elif t <= 3e+55:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (t <= -3.4e+23)
		tmp = Float64(x * t);
	elseif (t <= -3.8e-49)
		tmp = Float64(y * 5.0);
	elseif (t <= -7.4e-121)
		tmp = t_1;
	elseif (t <= -1.35e-211)
		tmp = Float64(y * 5.0);
	elseif (t <= 5.5e-189)
		tmp = t_1;
	elseif (t <= 1.7e-55)
		tmp = Float64(y * 5.0);
	elseif (t <= 3e+55)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (t <= -3.4e+23)
		tmp = x * t;
	elseif (t <= -3.8e-49)
		tmp = y * 5.0;
	elseif (t <= -7.4e-121)
		tmp = t_1;
	elseif (t <= -1.35e-211)
		tmp = y * 5.0;
	elseif (t <= 5.5e-189)
		tmp = t_1;
	elseif (t <= 1.7e-55)
		tmp = y * 5.0;
	elseif (t <= 3e+55)
		tmp = t_1;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+23], N[(x * t), $MachinePrecision], If[LessEqual[t, -3.8e-49], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, -7.4e-121], t$95$1, If[LessEqual[t, -1.35e-211], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 5.5e-189], t$95$1, If[LessEqual[t, 1.7e-55], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 3e+55], t$95$1, N[(x * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.39999999999999992e23 or 3.00000000000000017e55 < 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 58.1%

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

   if -3.39999999999999992e23 < t < -3.7999999999999997e-49 or -7.4000000000000004e-121 < t < -1.35e-211 or 5.4999999999999999e-189 < t < 1.69999999999999986e-55

   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 53.7%

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

   if -3.7999999999999997e-49 < t < -7.4000000000000004e-121 or -1.35e-211 < t < 5.4999999999999999e-189 or 1.69999999999999986e-55 < t < 3.00000000000000017e55

   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 54.0%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+23}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-49}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-121}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-211}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-189}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 3: 54.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := y \cdot \left(5 + x\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-167}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-287}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-18}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))) (t_2 (* y (+ 5.0 x))))
   (if (<= y -2.3e-29)
     t_2
     (if (<= y -1.4e-167)
       (* x t)
       (if (<= y -3.5e-230)
         t_1
         (if (<= y 1.1e-287)
           (* x t)
           (if (<= y 6.5e-150) t_1 (if (<= y 9.2e-18) (* x t) 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);
	double tmp;
	if (y <= -2.3e-29) {
		tmp = t_2;
	} else if (y <= -1.4e-167) {
		tmp = x * t;
	} else if (y <= -3.5e-230) {
		tmp = t_1;
	} else if (y <= 1.1e-287) {
		tmp = x * t;
	} else if (y <= 6.5e-150) {
		tmp = t_1;
	} else if (y <= 9.2e-18) {
		tmp = x * t;
	} 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)
    if (y <= (-2.3d-29)) then
        tmp = t_2
    else if (y <= (-1.4d-167)) then
        tmp = x * t
    else if (y <= (-3.5d-230)) then
        tmp = t_1
    else if (y <= 1.1d-287) then
        tmp = x * t
    else if (y <= 6.5d-150) then
        tmp = t_1
    else if (y <= 9.2d-18) then
        tmp = x * t
    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);
	double tmp;
	if (y <= -2.3e-29) {
		tmp = t_2;
	} else if (y <= -1.4e-167) {
		tmp = x * t;
	} else if (y <= -3.5e-230) {
		tmp = t_1;
	} else if (y <= 1.1e-287) {
		tmp = x * t;
	} else if (y <= 6.5e-150) {
		tmp = t_1;
	} else if (y <= 9.2e-18) {
		tmp = x * t;
	} 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)
	tmp = 0
	if y <= -2.3e-29:
		tmp = t_2
	elif y <= -1.4e-167:
		tmp = x * t
	elif y <= -3.5e-230:
		tmp = t_1
	elif y <= 1.1e-287:
		tmp = x * t
	elif y <= 6.5e-150:
		tmp = t_1
	elif y <= 9.2e-18:
		tmp = x * t
	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 + x))
	tmp = 0.0
	if (y <= -2.3e-29)
		tmp = t_2;
	elseif (y <= -1.4e-167)
		tmp = Float64(x * t);
	elseif (y <= -3.5e-230)
		tmp = t_1;
	elseif (y <= 1.1e-287)
		tmp = Float64(x * t);
	elseif (y <= 6.5e-150)
		tmp = t_1;
	elseif (y <= 9.2e-18)
		tmp = Float64(x * t);
	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);
	tmp = 0.0;
	if (y <= -2.3e-29)
		tmp = t_2;
	elseif (y <= -1.4e-167)
		tmp = x * t;
	elseif (y <= -3.5e-230)
		tmp = t_1;
	elseif (y <= 1.1e-287)
		tmp = x * t;
	elseif (y <= 6.5e-150)
		tmp = t_1;
	elseif (y <= 9.2e-18)
		tmp = x * t;
	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 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e-29], t$95$2, If[LessEqual[y, -1.4e-167], N[(x * t), $MachinePrecision], If[LessEqual[y, -3.5e-230], t$95$1, If[LessEqual[y, 1.1e-287], N[(x * t), $MachinePrecision], If[LessEqual[y, 6.5e-150], t$95$1, If[LessEqual[y, 9.2e-18], N[(x * t), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999991e-29 or 9.2000000000000004e-18 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 89.7%

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

   3. Taylor expanded in y around inf 66.1%

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

      1. +-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -2.29999999999999991e-29 < y < -1.39999999999999993e-167 or -3.49999999999999988e-230 < y < 1.1e-287 or 6.49999999999999997e-150 < y < 9.2000000000000004e-18

   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 55.8%

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

   if -1.39999999999999993e-167 < y < -3.49999999999999988e-230 or 1.1e-287 < y < 6.49999999999999997e-150

   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 69.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-167}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-230}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-287}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-150}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-18}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \end{array} \]

Alternative 4: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-242}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 5 + z \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (+ (* y 2.0) (* z 2.0))))))
   (if (<= x -1.05e-57)
     t_1
     (if (<= x 5e-242)
       (+ (* y 5.0) (* x t))
       (if (<= x 2.65e-53) (+ (* y 5.0) (* z (* x 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y * 2.0) + (z * 2.0)));
	double tmp;
	if (x <= -1.05e-57) {
		tmp = t_1;
	} else if (x <= 5e-242) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 2.65e-53) {
		tmp = (y * 5.0) + (z * (x * 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 = x * (t + ((y * 2.0d0) + (z * 2.0d0)))
    if (x <= (-1.05d-57)) then
        tmp = t_1
    else if (x <= 5d-242) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 2.65d-53) then
        tmp = (y * 5.0d0) + (z * (x * 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 = x * (t + ((y * 2.0) + (z * 2.0)));
	double tmp;
	if (x <= -1.05e-57) {
		tmp = t_1;
	} else if (x <= 5e-242) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 2.65e-53) {
		tmp = (y * 5.0) + (z * (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y * 2.0) + (z * 2.0)))
	tmp = 0
	if x <= -1.05e-57:
		tmp = t_1
	elif x <= 5e-242:
		tmp = (y * 5.0) + (x * t)
	elif x <= 2.65e-53:
		tmp = (y * 5.0) + (z * (x * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y * 2.0) + Float64(z * 2.0))))
	tmp = 0.0
	if (x <= -1.05e-57)
		tmp = t_1;
	elseif (x <= 5e-242)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 2.65e-53)
		tmp = Float64(Float64(y * 5.0) + Float64(z * Float64(x * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y * 2.0) + (z * 2.0)));
	tmp = 0.0;
	if (x <= -1.05e-57)
		tmp = t_1;
	elseif (x <= 5e-242)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 2.65e-53)
		tmp = (y * 5.0) + (z * (x * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(N[(y * 2.0), $MachinePrecision] + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e-57], t$95$1, If[LessEqual[x, 5e-242], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.65e-53], N[(N[(y * 5.0), $MachinePrecision] + N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e-57 or 2.65e-53 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 95.7%

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

   if -1.05e-57 < x < 4.9999999999999998e-242

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 87.8%

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

      1. +-commutative 87.8%

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

      2. distribute-lft-in 87.8%

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

      3. flip-+ 0.0%

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

      4. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{\color{blue}{0}}{y - y}\right) + y \cdot 5 \]

      5. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{0}{\color{blue}{0}}\right) + y \cdot 5 \]

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(x \cdot t + x \cdot \frac{0}{0}\right)} + y \cdot 5 \]

   6. Simplified 87.8%

      \[\leadsto \color{blue}{x \cdot \left(t + 0\right)} + y \cdot 5 \]

   7. Taylor expanded in x around 0 87.8%

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

   if 4.9999999999999998e-242 < x < 2.65e-53

   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. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      5. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      7. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      8. metadata-eval 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 86.0%

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

   6. Simplified 86.0%

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

      1. fma-udef 86.0%

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

      2. +-commutative 86.0%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

   8. Applied egg-rr 86.0%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-242}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 5 + z \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \end{array} \]

Alternative 5: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-244}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 5 + z \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (+ (* y 2.0) (* z 2.0))))))
   (if (<= x -3.9e-60)
     t_1
     (if (<= x 1.25e-244)
       (+ (* y 5.0) (* x (+ t (+ y y))))
       (if (<= x 5.2e-55) (+ (* y 5.0) (* z (* x 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((y * 2.0) + (z * 2.0)));
	double tmp;
	if (x <= -3.9e-60) {
		tmp = t_1;
	} else if (x <= 1.25e-244) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else if (x <= 5.2e-55) {
		tmp = (y * 5.0) + (z * (x * 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 = x * (t + ((y * 2.0d0) + (z * 2.0d0)))
    if (x <= (-3.9d-60)) then
        tmp = t_1
    else if (x <= 1.25d-244) then
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    else if (x <= 5.2d-55) then
        tmp = (y * 5.0d0) + (z * (x * 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 = x * (t + ((y * 2.0) + (z * 2.0)));
	double tmp;
	if (x <= -3.9e-60) {
		tmp = t_1;
	} else if (x <= 1.25e-244) {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	} else if (x <= 5.2e-55) {
		tmp = (y * 5.0) + (z * (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((y * 2.0) + (z * 2.0)))
	tmp = 0
	if x <= -3.9e-60:
		tmp = t_1
	elif x <= 1.25e-244:
		tmp = (y * 5.0) + (x * (t + (y + y)))
	elif x <= 5.2e-55:
		tmp = (y * 5.0) + (z * (x * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(y * 2.0) + Float64(z * 2.0))))
	tmp = 0.0
	if (x <= -3.9e-60)
		tmp = t_1;
	elseif (x <= 1.25e-244)
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	elseif (x <= 5.2e-55)
		tmp = Float64(Float64(y * 5.0) + Float64(z * Float64(x * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + ((y * 2.0) + (z * 2.0)));
	tmp = 0.0;
	if (x <= -3.9e-60)
		tmp = t_1;
	elseif (x <= 1.25e-244)
		tmp = (y * 5.0) + (x * (t + (y + y)));
	elseif (x <= 5.2e-55)
		tmp = (y * 5.0) + (z * (x * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(N[(y * 2.0), $MachinePrecision] + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e-60], t$95$1, If[LessEqual[x, 1.25e-244], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e-55], N[(N[(y * 5.0), $MachinePrecision] + N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9000000000000002e-60 or 5.1999999999999998e-55 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 95.7%

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

   if -3.9000000000000002e-60 < x < 1.24999999999999999e-244

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 87.8%

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

   if 1.24999999999999999e-244 < x < 5.1999999999999998e-55

   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. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      5. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      7. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      8. metadata-eval 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 86.0%

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

   6. Simplified 86.0%

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

      1. fma-udef 86.0%

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

      2. +-commutative 86.0%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

   8. Applied egg-rr 86.0%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-244}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 5 + z \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \end{array} \]

Alternative 6: 98.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+22} \lor \neg \left(x \leq 0.0011\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + z \cdot 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.75e+22) (not (<= x 0.0011)))
   (* x (+ t (+ (* y 2.0) (* z 2.0))))
   (+ (* y 5.0) (* x (+ t (+ y (* z 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e+22) || !(x <= 0.0011)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (z * 2.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.75d+22)) .or. (.not. (x <= 0.0011d0))) then
        tmp = x * (t + ((y * 2.0d0) + (z * 2.0d0)))
    else
        tmp = (y * 5.0d0) + (x * (t + (y + (z * 2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e+22) || !(x <= 0.0011)) {
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (z * 2.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.75e+22) or not (x <= 0.0011):
		tmp = x * (t + ((y * 2.0) + (z * 2.0)))
	else:
		tmp = (y * 5.0) + (x * (t + (y + (z * 2.0))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.75e+22) || !(x <= 0.0011))
		tmp = Float64(x * Float64(t + Float64(Float64(y * 2.0) + Float64(z * 2.0))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + Float64(z * 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.75e+22) || ~((x <= 0.0011)))
		tmp = x * (t + ((y * 2.0) + (z * 2.0)));
	else
		tmp = (y * 5.0) + (x * (t + (y + (z * 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.75e+22], N[Not[LessEqual[x, 0.0011]], $MachinePrecision]], N[(x * N[(t + N[(N[(y * 2.0), $MachinePrecision] + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75e22 or 0.00110000000000000007 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   if -1.75e22 < x < 0.00110000000000000007

   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 99.1%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+22} \lor \neg \left(x \leq 0.0011\right):\\ \;\;\;\;x \cdot \left(t + \left(y \cdot 2 + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + z \cdot 2\right)\right)\\ \end{array} \]

Alternative 7: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-166}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -7e+72)
     t_2
     (if (<= y -1.35e-133)
       t_1
       (if (<= y -2.1e-166)
         (+ (* y 5.0) (* x t))
         (if (<= y 1.3e-17) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -7e+72) {
		tmp = t_2;
	} else if (y <= -1.35e-133) {
		tmp = t_1;
	} else if (y <= -2.1e-166) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.3e-17) {
		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 = x * (t + (z * 2.0d0))
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-7d+72)) then
        tmp = t_2
    else if (y <= (-1.35d-133)) then
        tmp = t_1
    else if (y <= (-2.1d-166)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 1.3d-17) 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 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -7e+72) {
		tmp = t_2;
	} else if (y <= -1.35e-133) {
		tmp = t_1;
	} else if (y <= -2.1e-166) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.3e-17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -7e+72:
		tmp = t_2
	elif y <= -1.35e-133:
		tmp = t_1
	elif y <= -2.1e-166:
		tmp = (y * 5.0) + (x * t)
	elif y <= 1.3e-17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -7e+72)
		tmp = t_2;
	elseif (y <= -1.35e-133)
		tmp = t_1;
	elseif (y <= -2.1e-166)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 1.3e-17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -7e+72)
		tmp = t_2;
	elseif (y <= -1.35e-133)
		tmp = t_1;
	elseif (y <= -2.1e-166)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 1.3e-17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+72], t$95$2, If[LessEqual[y, -1.35e-133], t$95$1, If[LessEqual[y, -2.1e-166], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-17], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000002e72 or 1.30000000000000002e-17 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 80.1%

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

   4. Simplified 80.1%

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

   if -7.0000000000000002e72 < y < -1.3499999999999999e-133 or -2.0999999999999999e-166 < y < 1.30000000000000002e-17

   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 83.9%

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

   if -1.3499999999999999e-133 < y < -2.0999999999999999e-166

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 92.8%

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

      1. +-commutative 92.8%

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

      2. distribute-lft-in 92.8%

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

      3. flip-+ 0.0%

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

      4. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{\color{blue}{0}}{y - y}\right) + y \cdot 5 \]

      5. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{0}{\color{blue}{0}}\right) + y \cdot 5 \]

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(x \cdot t + x \cdot \frac{0}{0}\right)} + y \cdot 5 \]

   6. Simplified 92.8%

      \[\leadsto \color{blue}{x \cdot \left(t + 0\right)} + y \cdot 5 \]

   7. Taylor expanded in x around 0 92.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-166}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 8: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(y + z \cdot 2\right)\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-248}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 5 + z \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (+ y (* z 2.0))))))
   (if (<= x -1.05e-57)
     t_1
     (if (<= x 4.6e-248)
       (+ (* y 5.0) (* x t))
       (if (<= x 1.65e-53) (+ (* y 5.0) (* z (* x 2.0))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y + (z * 2.0)));
	double tmp;
	if (x <= -1.05e-57) {
		tmp = t_1;
	} else if (x <= 4.6e-248) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.65e-53) {
		tmp = (y * 5.0) + (z * (x * 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 = x * (t + (y + (z * 2.0d0)))
    if (x <= (-1.05d-57)) then
        tmp = t_1
    else if (x <= 4.6d-248) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 1.65d-53) then
        tmp = (y * 5.0d0) + (z * (x * 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 = x * (t + (y + (z * 2.0)));
	double tmp;
	if (x <= -1.05e-57) {
		tmp = t_1;
	} else if (x <= 4.6e-248) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 1.65e-53) {
		tmp = (y * 5.0) + (z * (x * 2.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y + (z * 2.0)))
	tmp = 0
	if x <= -1.05e-57:
		tmp = t_1
	elif x <= 4.6e-248:
		tmp = (y * 5.0) + (x * t)
	elif x <= 1.65e-53:
		tmp = (y * 5.0) + (z * (x * 2.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y + Float64(z * 2.0))))
	tmp = 0.0
	if (x <= -1.05e-57)
		tmp = t_1;
	elseif (x <= 4.6e-248)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 1.65e-53)
		tmp = Float64(Float64(y * 5.0) + Float64(z * Float64(x * 2.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y + (z * 2.0)));
	tmp = 0.0;
	if (x <= -1.05e-57)
		tmp = t_1;
	elseif (x <= 4.6e-248)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 1.65e-53)
		tmp = (y * 5.0) + (z * (x * 2.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e-57], t$95$1, If[LessEqual[x, 4.6e-248], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e-53], N[(N[(y * 5.0), $MachinePrecision] + N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e-57 or 1.65000000000000002e-53 < 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 87.7%

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

   3. Taylor expanded in x around inf 84.2%

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

   if -1.05e-57 < x < 4.6e-248

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 87.8%

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

      1. +-commutative 87.8%

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

      2. distribute-lft-in 87.8%

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

      3. flip-+ 0.0%

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

      4. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{\color{blue}{0}}{y - y}\right) + y \cdot 5 \]

      5. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{0}{\color{blue}{0}}\right) + y \cdot 5 \]

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(x \cdot t + x \cdot \frac{0}{0}\right)} + y \cdot 5 \]

   6. Simplified 87.8%

      \[\leadsto \color{blue}{x \cdot \left(t + 0\right)} + y \cdot 5 \]

   7. Taylor expanded in x around 0 87.8%

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

   if 4.6e-248 < x < 1.65000000000000002e-53

   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. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(\color{blue}{1 \cdot \left(y + z\right)} + \left(z + y\right)\right) + t\right)\right) \]

      5. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right)\right) \]

      6. *-un-lft-identity 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\left(1 \cdot \left(y + z\right) + \color{blue}{1 \cdot \left(y + z\right)}\right) + t\right)\right) \]

      7. distribute-rgt-out 100.0%

         \[\leadsto \mathsf{fma}\left(y, 5, x \cdot \left(\color{blue}{\left(y + z\right) \cdot \left(1 + 1\right)} + t\right)\right) \]

      8. metadata-eval 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 86.0%

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

   6. Simplified 86.0%

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

      1. fma-udef 86.0%

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

      2. +-commutative 86.0%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

   8. Applied egg-rr 86.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-248}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 5 + z \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right)\\ \end{array} \]

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 10: 80.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-58} \lor \neg \left(x \leq 3.1 \cdot 10^{-116}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.5e-58) (not (<= x 3.1e-116)))
   (* 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 <= -4.5e-58) || !(x <= 3.1e-116)) {
		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 <= (-4.5d-58)) .or. (.not. (x <= 3.1d-116))) 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 <= -4.5e-58) || !(x <= 3.1e-116)) {
		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 <= -4.5e-58) or not (x <= 3.1e-116):
		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 <= -4.5e-58) || !(x <= 3.1e-116))
		tmp = Float64(x * Float64(t + Float64(y + Float64(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 <= -4.5e-58) || ~((x <= 3.1e-116)))
		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, -4.5e-58], N[Not[LessEqual[x, 3.1e-116]], $MachinePrecision]], N[(x * N[(t + N[(y + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000003e-58 or 3.10000000000000018e-116 < 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 88.7%

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

   3. Taylor expanded in x around inf 82.5%

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

   if -4.5000000000000003e-58 < x < 3.10000000000000018e-116

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 85.6%

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

      1. +-commutative 85.6%

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

      2. distribute-lft-in 85.6%

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

      3. flip-+ 0.0%

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

      4. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{\color{blue}{0}}{y - y}\right) + y \cdot 5 \]

      5. +-inverses 0.0%

         \[\leadsto \left(x \cdot t + x \cdot \frac{0}{\color{blue}{0}}\right) + y \cdot 5 \]

   4. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\left(x \cdot t + x \cdot \frac{0}{0}\right)} + y \cdot 5 \]

   6. Simplified 85.6%

      \[\leadsto \color{blue}{x \cdot \left(t + 0\right)} + y \cdot 5 \]

   7. Taylor expanded in x around 0 85.6%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-58} \lor \neg \left(x \leq 3.1 \cdot 10^{-116}\right):\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]

Alternative 11: 74.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+71} \lor \neg \left(y \leq 9.2 \cdot 10^{+38}\right):\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.1e+71) (not (<= y 9.2e+38)))
   (* y (+ 5.0 x))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e+71) || !(y <= 9.2e+38)) {
		tmp = y * (5.0 + x);
	} 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 <= (-3.1d+71)) .or. (.not. (y <= 9.2d+38))) then
        tmp = y * (5.0d0 + x)
    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 <= -3.1e+71) || !(y <= 9.2e+38)) {
		tmp = y * (5.0 + x);
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.1e+71) or not (y <= 9.2e+38):
		tmp = y * (5.0 + x)
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.1e+71) || !(y <= 9.2e+38))
		tmp = Float64(y * Float64(5.0 + x));
	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 <= -3.1e+71) || ~((y <= 9.2e+38)))
		tmp = y * (5.0 + x);
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.1e+71], N[Not[LessEqual[y, 9.2e+38]], $MachinePrecision]], N[(y * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000018e71 or 9.2000000000000005e38 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 90.8%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. +-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -3.10000000000000018e71 < y < 9.2000000000000005e38

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.8%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+71} \lor \neg \left(y \leq 9.2 \cdot 10^{+38}\right):\\ \;\;\;\;y \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 12: 77.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+71} \lor \neg \left(y \leq 1.7 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.15e+71) (not (<= y 1.7e-18)))
   (* 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 <= -2.15e+71) || !(y <= 1.7e-18)) {
		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 <= (-2.15d+71)) .or. (.not. (y <= 1.7d-18))) 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 <= -2.15e+71) || !(y <= 1.7e-18)) {
		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 <= -2.15e+71) or not (y <= 1.7e-18):
		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 <= -2.15e+71) || !(y <= 1.7e-18))
		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 <= -2.15e+71) || ~((y <= 1.7e-18)))
		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, -2.15e+71], N[Not[LessEqual[y, 1.7e-18]], $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 < -2.14999999999999992e71 or 1.70000000000000001e-18 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 80.1%

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

   4. Simplified 80.1%

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

   if -2.14999999999999992e71 < y < 1.70000000000000001e-18

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+71} \lor \neg \left(y \leq 1.7 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 13: 43.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+20} \lor \neg \left(t \leq 7 \cdot 10^{-49}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.6e+20) (not (<= t 7e-49))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.6e+20) || !(t <= 7e-49)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.6d+20)) .or. (.not. (t <= 7d-49))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.6e+20) || !(t <= 7e-49)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.6e+20) or not (t <= 7e-49):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.6e+20) || !(t <= 7e-49))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.6e+20) || ~((t <= 7e-49)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.6e+20], N[Not[LessEqual[t, 7e-49]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e20 or 7.00000000000000012e-49 < 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 52.2%

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

   if -2.6e20 < t < 7.00000000000000012e-49

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 37.4%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+20} \lor \neg \left(t \leq 7 \cdot 10^{-49}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 14: 29.8% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 26.3%

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

3. Final simplification 26.3%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023322 
(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)))