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

Percentage Accurate: 99.9% → 99.9%

Time: 9.6s

Alternatives: 11

Speedup: 0.1×

• 26.4% 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: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

5. Final simplification 99.9%

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

Alternative 2: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ t_2 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-30}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+52} \lor \neg \left(x \leq 1.96 \cdot 10^{+167}\right) \land x \leq 2.7 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))) (t_2 (* x (* 2.0 (+ y z)))))
   (if (<= x -3e+188)
     t_2
     (if (<= x -5.5e-68)
       t_1
       (if (<= x 5e-126)
         (* y 5.0)
         (if (<= x 8e-81)
           t_1
           (if (<= x 2.85e-30)
             (* y 5.0)
             (if (or (<= x 2.3e+52)
                     (and (not (<= x 1.96e+167)) (<= x 2.7e+206)))
               t_1
               t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -3e+188) {
		tmp = t_2;
	} else if (x <= -5.5e-68) {
		tmp = t_1;
	} else if (x <= 5e-126) {
		tmp = y * 5.0;
	} else if (x <= 8e-81) {
		tmp = t_1;
	} else if (x <= 2.85e-30) {
		tmp = y * 5.0;
	} else if ((x <= 2.3e+52) || (!(x <= 1.96e+167) && (x <= 2.7e+206))) {
		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 + (2.0d0 * z))
    t_2 = x * (2.0d0 * (y + z))
    if (x <= (-3d+188)) then
        tmp = t_2
    else if (x <= (-5.5d-68)) then
        tmp = t_1
    else if (x <= 5d-126) then
        tmp = y * 5.0d0
    else if (x <= 8d-81) then
        tmp = t_1
    else if (x <= 2.85d-30) then
        tmp = y * 5.0d0
    else if ((x <= 2.3d+52) .or. (.not. (x <= 1.96d+167)) .and. (x <= 2.7d+206)) 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 + (2.0 * z));
	double t_2 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -3e+188) {
		tmp = t_2;
	} else if (x <= -5.5e-68) {
		tmp = t_1;
	} else if (x <= 5e-126) {
		tmp = y * 5.0;
	} else if (x <= 8e-81) {
		tmp = t_1;
	} else if (x <= 2.85e-30) {
		tmp = y * 5.0;
	} else if ((x <= 2.3e+52) || (!(x <= 1.96e+167) && (x <= 2.7e+206))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * z))
	t_2 = x * (2.0 * (y + z))
	tmp = 0
	if x <= -3e+188:
		tmp = t_2
	elif x <= -5.5e-68:
		tmp = t_1
	elif x <= 5e-126:
		tmp = y * 5.0
	elif x <= 8e-81:
		tmp = t_1
	elif x <= 2.85e-30:
		tmp = y * 5.0
	elif (x <= 2.3e+52) or (not (x <= 1.96e+167) and (x <= 2.7e+206)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * z)))
	t_2 = Float64(x * Float64(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -3e+188)
		tmp = t_2;
	elseif (x <= -5.5e-68)
		tmp = t_1;
	elseif (x <= 5e-126)
		tmp = Float64(y * 5.0);
	elseif (x <= 8e-81)
		tmp = t_1;
	elseif (x <= 2.85e-30)
		tmp = Float64(y * 5.0);
	elseif ((x <= 2.3e+52) || (!(x <= 1.96e+167) && (x <= 2.7e+206)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * z));
	t_2 = x * (2.0 * (y + z));
	tmp = 0.0;
	if (x <= -3e+188)
		tmp = t_2;
	elseif (x <= -5.5e-68)
		tmp = t_1;
	elseif (x <= 5e-126)
		tmp = y * 5.0;
	elseif (x <= 8e-81)
		tmp = t_1;
	elseif (x <= 2.85e-30)
		tmp = y * 5.0;
	elseif ((x <= 2.3e+52) || (~((x <= 1.96e+167)) && (x <= 2.7e+206)))
		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[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+188], t$95$2, If[LessEqual[x, -5.5e-68], t$95$1, If[LessEqual[x, 5e-126], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 8e-81], t$95$1, If[LessEqual[x, 2.85e-30], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 2.3e+52], And[N[Not[LessEqual[x, 1.96e+167]], $MachinePrecision], LessEqual[x, 2.7e+206]]], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0000000000000001e188 or 2.3e52 < x < 1.95999999999999988e167 or 2.70000000000000003e206 < 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. Add Preprocessing

   3. Taylor expanded in t around 0 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in x around inf 88.7%

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

      1. associate-*r* 88.7%

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

      2. *-commutative 88.7%

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

      3. +-commutative 88.7%

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

      4. associate-*r* 88.7%

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

      5. +-commutative 88.7%

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

   8. Simplified 88.7%

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

   if -3.0000000000000001e188 < x < -5.5000000000000003e-68 or 5.00000000000000006e-126 < x < 7.9999999999999997e-81 or 2.84999999999999989e-30 < x < 2.3e52 or 1.95999999999999988e167 < x < 2.70000000000000003e206

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 76.6%

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

   5. Simplified 76.6%

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

   if -5.5000000000000003e-68 < x < 5.00000000000000006e-126 or 7.9999999999999997e-81 < x < 2.84999999999999989e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 72.2%

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

   5. Simplified 72.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-30}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+52} \lor \neg \left(x \leq 1.96 \cdot 10^{+167}\right) \land x \leq 2.7 \cdot 10^{+206}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{if}\;x \leq -2.55 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+91}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-91}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* 2.0 (+ y z)))))
   (if (<= x -2.55e+123)
     t_1
     (if (<= x -9e+91)
       (* x t)
       (if (<= x -1e-63)
         t_1
         (if (<= x 5e-126)
           (* y 5.0)
           (if (<= x 1.1e-91)
             (* x t)
             (if (<= x 2.5e-30)
               (* y 5.0)
               (if (<= x 6.8e+45) (* x t) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -2.55e+123) {
		tmp = t_1;
	} else if (x <= -9e+91) {
		tmp = x * t;
	} else if (x <= -1e-63) {
		tmp = t_1;
	} else if (x <= 5e-126) {
		tmp = y * 5.0;
	} else if (x <= 1.1e-91) {
		tmp = x * t;
	} else if (x <= 2.5e-30) {
		tmp = y * 5.0;
	} else if (x <= 6.8e+45) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (2.0d0 * (y + z))
    if (x <= (-2.55d+123)) then
        tmp = t_1
    else if (x <= (-9d+91)) then
        tmp = x * t
    else if (x <= (-1d-63)) then
        tmp = t_1
    else if (x <= 5d-126) then
        tmp = y * 5.0d0
    else if (x <= 1.1d-91) then
        tmp = x * t
    else if (x <= 2.5d-30) then
        tmp = y * 5.0d0
    else if (x <= 6.8d+45) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (2.0 * (y + z));
	double tmp;
	if (x <= -2.55e+123) {
		tmp = t_1;
	} else if (x <= -9e+91) {
		tmp = x * t;
	} else if (x <= -1e-63) {
		tmp = t_1;
	} else if (x <= 5e-126) {
		tmp = y * 5.0;
	} else if (x <= 1.1e-91) {
		tmp = x * t;
	} else if (x <= 2.5e-30) {
		tmp = y * 5.0;
	} else if (x <= 6.8e+45) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (2.0 * (y + z))
	tmp = 0
	if x <= -2.55e+123:
		tmp = t_1
	elif x <= -9e+91:
		tmp = x * t
	elif x <= -1e-63:
		tmp = t_1
	elif x <= 5e-126:
		tmp = y * 5.0
	elif x <= 1.1e-91:
		tmp = x * t
	elif x <= 2.5e-30:
		tmp = y * 5.0
	elif x <= 6.8e+45:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(2.0 * Float64(y + z)))
	tmp = 0.0
	if (x <= -2.55e+123)
		tmp = t_1;
	elseif (x <= -9e+91)
		tmp = Float64(x * t);
	elseif (x <= -1e-63)
		tmp = t_1;
	elseif (x <= 5e-126)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.1e-91)
		tmp = Float64(x * t);
	elseif (x <= 2.5e-30)
		tmp = Float64(y * 5.0);
	elseif (x <= 6.8e+45)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (2.0 * (y + z));
	tmp = 0.0;
	if (x <= -2.55e+123)
		tmp = t_1;
	elseif (x <= -9e+91)
		tmp = x * t;
	elseif (x <= -1e-63)
		tmp = t_1;
	elseif (x <= 5e-126)
		tmp = y * 5.0;
	elseif (x <= 1.1e-91)
		tmp = x * t;
	elseif (x <= 2.5e-30)
		tmp = y * 5.0;
	elseif (x <= 6.8e+45)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.55e+123], t$95$1, If[LessEqual[x, -9e+91], N[(x * t), $MachinePrecision], If[LessEqual[x, -1e-63], t$95$1, If[LessEqual[x, 5e-126], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.1e-91], N[(x * t), $MachinePrecision], If[LessEqual[x, 2.5e-30], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 6.8e+45], N[(x * t), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.54999999999999986e123 or -9e91 < x < -1.00000000000000007e-63 or 6.8e45 < 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. Add Preprocessing

   3. Taylor expanded in t around 0 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in x around inf 78.0%

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

      1. associate-*r* 78.0%

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

      2. *-commutative 78.0%

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

      3. +-commutative 78.0%

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

      4. associate-*r* 78.0%

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

      5. +-commutative 78.0%

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

   8. Simplified 78.0%

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

   if -2.54999999999999986e123 < x < -9e91 or 5.00000000000000006e-126 < x < 1.1e-91 or 2.49999999999999986e-30 < x < 6.8e45

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 70.7%

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

   5. Simplified 70.7%

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

   if -1.00000000000000007e-63 < x < 5.00000000000000006e-126 or 1.1e-91 < x < 2.49999999999999986e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 72.2%

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

   5. Simplified 72.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+91}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-91}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-32}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+103}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= x -4e+193)
     t_1
     (if (<= x -1.4e+39)
       (* x t)
       (if (<= x -3e-55)
         t_1
         (if (<= x 4.6e-126)
           (* y 5.0)
           (if (<= x 9.5e-84)
             (* x t)
             (if (<= x 1.2e-32)
               (* y 5.0)
               (if (<= x 1.4e+103) (* x t) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -4e+193) {
		tmp = t_1;
	} else if (x <= -1.4e+39) {
		tmp = x * t;
	} else if (x <= -3e-55) {
		tmp = t_1;
	} else if (x <= 4.6e-126) {
		tmp = y * 5.0;
	} else if (x <= 9.5e-84) {
		tmp = x * t;
	} else if (x <= 1.2e-32) {
		tmp = y * 5.0;
	} else if (x <= 1.4e+103) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (x <= (-4d+193)) then
        tmp = t_1
    else if (x <= (-1.4d+39)) then
        tmp = x * t
    else if (x <= (-3d-55)) then
        tmp = t_1
    else if (x <= 4.6d-126) then
        tmp = y * 5.0d0
    else if (x <= 9.5d-84) then
        tmp = x * t
    else if (x <= 1.2d-32) then
        tmp = y * 5.0d0
    else if (x <= 1.4d+103) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (x <= -4e+193) {
		tmp = t_1;
	} else if (x <= -1.4e+39) {
		tmp = x * t;
	} else if (x <= -3e-55) {
		tmp = t_1;
	} else if (x <= 4.6e-126) {
		tmp = y * 5.0;
	} else if (x <= 9.5e-84) {
		tmp = x * t;
	} else if (x <= 1.2e-32) {
		tmp = y * 5.0;
	} else if (x <= 1.4e+103) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if x <= -4e+193:
		tmp = t_1
	elif x <= -1.4e+39:
		tmp = x * t
	elif x <= -3e-55:
		tmp = t_1
	elif x <= 4.6e-126:
		tmp = y * 5.0
	elif x <= 9.5e-84:
		tmp = x * t
	elif x <= 1.2e-32:
		tmp = y * 5.0
	elif x <= 1.4e+103:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (x <= -4e+193)
		tmp = t_1;
	elseif (x <= -1.4e+39)
		tmp = Float64(x * t);
	elseif (x <= -3e-55)
		tmp = t_1;
	elseif (x <= 4.6e-126)
		tmp = Float64(y * 5.0);
	elseif (x <= 9.5e-84)
		tmp = Float64(x * t);
	elseif (x <= 1.2e-32)
		tmp = Float64(y * 5.0);
	elseif (x <= 1.4e+103)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (x <= -4e+193)
		tmp = t_1;
	elseif (x <= -1.4e+39)
		tmp = x * t;
	elseif (x <= -3e-55)
		tmp = t_1;
	elseif (x <= 4.6e-126)
		tmp = y * 5.0;
	elseif (x <= 9.5e-84)
		tmp = x * t;
	elseif (x <= 1.2e-32)
		tmp = y * 5.0;
	elseif (x <= 1.4e+103)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+193], t$95$1, If[LessEqual[x, -1.4e+39], N[(x * t), $MachinePrecision], If[LessEqual[x, -3e-55], t$95$1, If[LessEqual[x, 4.6e-126], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 9.5e-84], N[(x * t), $MachinePrecision], If[LessEqual[x, 1.2e-32], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 1.4e+103], N[(x * t), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.00000000000000026e193 or -1.40000000000000001e39 < x < -3.00000000000000016e-55 or 1.40000000000000004e103 < 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. Add Preprocessing

   3. Taylor expanded in z around inf 51.0%

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

   5. Simplified 51.0%

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

   if -4.00000000000000026e193 < x < -1.40000000000000001e39 or 4.60000000000000021e-126 < x < 9.49999999999999941e-84 or 1.2000000000000001e-32 < x < 1.40000000000000004e103

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 50.6%

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

   5. Simplified 50.6%

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

   if -3.00000000000000016e-55 < x < 4.60000000000000021e-126 or 9.49999999999999941e-84 < x < 1.2000000000000001e-32

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 72.2%

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

   5. Simplified 72.2%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+193}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+39}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-55}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-126}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-32}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+103}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 26500000:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(y \cdot 5 + x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 26500000.0)
   (+ (* 2.0 (* x (+ y z))) (+ (* y 5.0) (* x t)))
   (* x (+ (* 2.0 (+ y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 26500000.0) {
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	} else {
		tmp = x * ((2.0 * (y + z)) + 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 <= 26500000.0d0) then
        tmp = (2.0d0 * (x * (y + z))) + ((y * 5.0d0) + (x * t))
    else
        tmp = x * ((2.0d0 * (y + z)) + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 26500000.0) {
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	} else {
		tmp = x * ((2.0 * (y + z)) + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 26500000.0:
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t))
	else:
		tmp = x * ((2.0 * (y + z)) + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 26500000.0)
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(Float64(y * 5.0) + Float64(x * t)));
	else
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 26500000.0)
		tmp = (2.0 * (x * (y + z))) + ((y * 5.0) + (x * t));
	else
		tmp = x * ((2.0 * (y + z)) + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 26500000.0], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.65e7

   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. Add Preprocessing

   5. Taylor expanded in t around 0 97.8%

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

   if 2.65e7 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 26500000:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + \left(y \cdot 5 + x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(y + z\right)\\ t_2 := x \cdot \left(t_1 + t\right)\\ \mathbf{if}\;x \leq -11000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-195}:\\ \;\;\;\;y \cdot 5 + x \cdot t_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ y z))) (t_2 (* x (+ t_1 t))))
   (if (<= x -11000000000.0)
     t_2
     (if (<= x 2.4e-195)
       (+ (* y 5.0) (* x t_1))
       (if (<= x 9.5e-24) (+ (* y 5.0) (* x t)) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (y + z);
	double t_2 = x * (t_1 + t);
	double tmp;
	if (x <= -11000000000.0) {
		tmp = t_2;
	} else if (x <= 2.4e-195) {
		tmp = (y * 5.0) + (x * t_1);
	} else if (x <= 9.5e-24) {
		tmp = (y * 5.0) + (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 * (y + z)
    t_2 = x * (t_1 + t)
    if (x <= (-11000000000.0d0)) then
        tmp = t_2
    else if (x <= 2.4d-195) then
        tmp = (y * 5.0d0) + (x * t_1)
    else if (x <= 9.5d-24) then
        tmp = (y * 5.0d0) + (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 * (y + z);
	double t_2 = x * (t_1 + t);
	double tmp;
	if (x <= -11000000000.0) {
		tmp = t_2;
	} else if (x <= 2.4e-195) {
		tmp = (y * 5.0) + (x * t_1);
	} else if (x <= 9.5e-24) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (y + z)
	t_2 = x * (t_1 + t)
	tmp = 0
	if x <= -11000000000.0:
		tmp = t_2
	elif x <= 2.4e-195:
		tmp = (y * 5.0) + (x * t_1)
	elif x <= 9.5e-24:
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(y + z))
	t_2 = Float64(x * Float64(t_1 + t))
	tmp = 0.0
	if (x <= -11000000000.0)
		tmp = t_2;
	elseif (x <= 2.4e-195)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t_1));
	elseif (x <= 9.5e-24)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (y + z);
	t_2 = x * (t_1 + t);
	tmp = 0.0;
	if (x <= -11000000000.0)
		tmp = t_2;
	elseif (x <= 2.4e-195)
		tmp = (y * 5.0) + (x * t_1);
	elseif (x <= 9.5e-24)
		tmp = (y * 5.0) + (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[(y + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t$95$1 + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -11000000000.0], t$95$2, If[LessEqual[x, 2.4e-195], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e-24], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e10 or 9.50000000000000029e-24 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.6%

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

   if -1.1e10 < x < 2.4e-195

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 88.7%

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

   5. Simplified 88.7%

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

   if 2.4e-195 < x < 9.50000000000000029e-24

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. 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. flip-+ 0.0%

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

      4. pow2 0.0%

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

      5. pow2 0.0%

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

   4. Applied egg-rr 0.0%

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

   6. Simplified 87.6%

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

   7. Taylor expanded in x around 0 87.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11000000000:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-195}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.9%

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

Alternative 8: 88.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-20} \lor \neg \left(x \leq 2.05 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.5e-20) (not (<= x 2.05e-32)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.5e-20) || !(x <= 2.05e-32)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} 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 <= (-7.5d-20)) .or. (.not. (x <= 2.05d-32))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    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 <= -7.5e-20) || !(x <= 2.05e-32)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.5e-20) or not (x <= 2.05e-32):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.5e-20) || !(x <= 2.05e-32))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	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 <= -7.5e-20) || ~((x <= 2.05e-32)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.5e-20], N[Not[LessEqual[x, 2.05e-32]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.49999999999999981e-20 or 2.04999999999999988e-32 < x

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 97.8%

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

   if -7.49999999999999981e-20 < x < 2.04999999999999988e-32

   1. Initial program 99.9%

      \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5 \]
   2. Add Preprocessing
   3. 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. flip-+ 0.0%

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

      4. pow2 0.0%

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

      5. pow2 0.0%

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

   4. Applied egg-rr 0.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in x around 0 82.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-20} \lor \neg \left(x \leq 2.05 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -11000000000 \lor \neg \left(x \leq 4.6 \cdot 10^{-126}\right) \land \left(x \leq 1.1 \cdot 10^{-90} \lor \neg \left(x \leq 3.7 \cdot 10^{-23}\right)\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -11000000000.0)
         (and (not (<= x 4.6e-126)) (or (<= x 1.1e-90) (not (<= x 3.7e-23)))))
   (* x t)
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -11000000000.0) || (!(x <= 4.6e-126) && ((x <= 1.1e-90) || !(x <= 3.7e-23)))) {
		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 ((x <= (-11000000000.0d0)) .or. (.not. (x <= 4.6d-126)) .and. (x <= 1.1d-90) .or. (.not. (x <= 3.7d-23))) 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 ((x <= -11000000000.0) || (!(x <= 4.6e-126) && ((x <= 1.1e-90) || !(x <= 3.7e-23)))) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -11000000000.0) or (not (x <= 4.6e-126) and ((x <= 1.1e-90) or not (x <= 3.7e-23))):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -11000000000.0) || (!(x <= 4.6e-126) && ((x <= 1.1e-90) || !(x <= 3.7e-23))))
		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 ((x <= -11000000000.0) || (~((x <= 4.6e-126)) && ((x <= 1.1e-90) || ~((x <= 3.7e-23)))))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -11000000000.0], And[N[Not[LessEqual[x, 4.6e-126]], $MachinePrecision], Or[LessEqual[x, 1.1e-90], N[Not[LessEqual[x, 3.7e-23]], $MachinePrecision]]]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e10 or 4.60000000000000021e-126 < x < 1.09999999999999993e-90 or 3.7000000000000003e-23 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 38.0%

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

   5. Simplified 38.0%

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

   if -1.1e10 < x < 4.60000000000000021e-126 or 1.09999999999999993e-90 < x < 3.7000000000000003e-23

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 68.3%

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

   5. Simplified 68.3%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11000000000 \lor \neg \left(x \leq 4.6 \cdot 10^{-126}\right) \land \left(x \leq 1.1 \cdot 10^{-90} \lor \neg \left(x \leq 3.7 \cdot 10^{-23}\right)\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+109} \lor \neg \left(y \leq 4.2 \cdot 10^{+56}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e+109) (not (<= y 4.2e+56)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+109) || !(y <= 4.2e+56)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9d+109)) .or. (.not. (y <= 4.2d+56))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (2.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+109) || !(y <= 4.2e+56)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e+109) or not (y <= 4.2e+56):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e+109) || !(y <= 4.2e+56))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9e+109) || ~((y <= 4.2e+56)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9e+109], N[Not[LessEqual[y, 4.2e+56]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999992e109 or 4.20000000000000034e56 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 86.2%

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

   if -8.9999999999999992e109 < y < 4.20000000000000034e56

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.2%

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

   5. Simplified 76.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+109} \lor \neg \left(y \leq 4.2 \cdot 10^{+56}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.9% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in t around inf 27.9%

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

5. Simplified 27.9%

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

6. Final simplification 27.9%

   \[\leadsto x \cdot t \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024011 
(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)))