Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 91.6% → 96.5%

Time: 8.6s

Alternatives: 13

Speedup: 0.4×

• 32.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 INFINITY) t_1 (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < +inf.0

   1. Initial program 96.7%

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

   if +inf.0 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 84.2%

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

4. Final simplification 95.8%

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

Alternative 2: 39.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-109}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.6e+59)
   x
   (if (<= x -5.8e-109)
     (* t a)
     (if (<= x -6.5e-248)
       (* z (* a b))
       (if (<= x 2.5e-196)
         (* y z)
         (if (<= x 1.8e-33) (* t a) (if (<= x 1.35e+105) (* a (* z b)) x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.6e+59) {
		tmp = x;
	} else if (x <= -5.8e-109) {
		tmp = t * a;
	} else if (x <= -6.5e-248) {
		tmp = z * (a * b);
	} else if (x <= 2.5e-196) {
		tmp = y * z;
	} else if (x <= 1.8e-33) {
		tmp = t * a;
	} else if (x <= 1.35e+105) {
		tmp = a * (z * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.6d+59)) then
        tmp = x
    else if (x <= (-5.8d-109)) then
        tmp = t * a
    else if (x <= (-6.5d-248)) then
        tmp = z * (a * b)
    else if (x <= 2.5d-196) then
        tmp = y * z
    else if (x <= 1.8d-33) then
        tmp = t * a
    else if (x <= 1.35d+105) then
        tmp = a * (z * b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.6e+59) {
		tmp = x;
	} else if (x <= -5.8e-109) {
		tmp = t * a;
	} else if (x <= -6.5e-248) {
		tmp = z * (a * b);
	} else if (x <= 2.5e-196) {
		tmp = y * z;
	} else if (x <= 1.8e-33) {
		tmp = t * a;
	} else if (x <= 1.35e+105) {
		tmp = a * (z * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.6e+59:
		tmp = x
	elif x <= -5.8e-109:
		tmp = t * a
	elif x <= -6.5e-248:
		tmp = z * (a * b)
	elif x <= 2.5e-196:
		tmp = y * z
	elif x <= 1.8e-33:
		tmp = t * a
	elif x <= 1.35e+105:
		tmp = a * (z * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.6e+59)
		tmp = x;
	elseif (x <= -5.8e-109)
		tmp = Float64(t * a);
	elseif (x <= -6.5e-248)
		tmp = Float64(z * Float64(a * b));
	elseif (x <= 2.5e-196)
		tmp = Float64(y * z);
	elseif (x <= 1.8e-33)
		tmp = Float64(t * a);
	elseif (x <= 1.35e+105)
		tmp = Float64(a * Float64(z * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.6e+59)
		tmp = x;
	elseif (x <= -5.8e-109)
		tmp = t * a;
	elseif (x <= -6.5e-248)
		tmp = z * (a * b);
	elseif (x <= 2.5e-196)
		tmp = y * z;
	elseif (x <= 1.8e-33)
		tmp = t * a;
	elseif (x <= 1.35e+105)
		tmp = a * (z * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.6e+59], x, If[LessEqual[x, -5.8e-109], N[(t * a), $MachinePrecision], If[LessEqual[x, -6.5e-248], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-196], N[(y * z), $MachinePrecision], If[LessEqual[x, 1.8e-33], N[(t * a), $MachinePrecision], If[LessEqual[x, 1.35e+105], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.5999999999999999e59 or 1.35000000000000008e105 < x

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 66.1%

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

   if -3.5999999999999999e59 < x < -5.8e-109 or 2.5000000000000002e-196 < x < 1.80000000000000017e-33

   1. Initial program 92.0%

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

   3. Taylor expanded in t around inf 49.9%

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

   if -5.8e-109 < x < -6.5e-248

   1. Initial program 92.6%

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

   3. Taylor expanded in z around inf 75.6%

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

   4. Taylor expanded in y around 0 57.7%

      \[\leadsto z \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -6.5e-248 < x < 2.5000000000000002e-196

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 47.5%

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

      1. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   if 1.80000000000000017e-33 < x < 1.35000000000000008e105

   1. Initial program 85.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 85.1%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)} \]

      2. associate-*r* 85.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}} \]

      3. pow2 85.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \color{blue}{{\left(\sqrt[3]{b}\right)}^{2}}\right) \cdot \sqrt[3]{b} \]

   4. Applied egg-rr 85.0%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot {\left(\sqrt[3]{b}\right)}^{2}\right) \cdot \sqrt[3]{b}} \]

   5. Taylor expanded in b around inf 44.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   7. Simplified 44.5%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-109}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-109}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-33}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= x -6.8e+56)
     x
     (if (<= x -4.3e-109)
       (* t a)
       (if (<= x -3.5e-244)
         t_1
         (if (<= x 1.2e-196)
           (* y z)
           (if (<= x 2e-33) (* t a) (if (<= x 2.6e+103) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (x <= -6.8e+56) {
		tmp = x;
	} else if (x <= -4.3e-109) {
		tmp = t * a;
	} else if (x <= -3.5e-244) {
		tmp = t_1;
	} else if (x <= 1.2e-196) {
		tmp = y * z;
	} else if (x <= 2e-33) {
		tmp = t * a;
	} else if (x <= 2.6e+103) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (x <= (-6.8d+56)) then
        tmp = x
    else if (x <= (-4.3d-109)) then
        tmp = t * a
    else if (x <= (-3.5d-244)) then
        tmp = t_1
    else if (x <= 1.2d-196) then
        tmp = y * z
    else if (x <= 2d-33) then
        tmp = t * a
    else if (x <= 2.6d+103) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (x <= -6.8e+56) {
		tmp = x;
	} else if (x <= -4.3e-109) {
		tmp = t * a;
	} else if (x <= -3.5e-244) {
		tmp = t_1;
	} else if (x <= 1.2e-196) {
		tmp = y * z;
	} else if (x <= 2e-33) {
		tmp = t * a;
	} else if (x <= 2.6e+103) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if x <= -6.8e+56:
		tmp = x
	elif x <= -4.3e-109:
		tmp = t * a
	elif x <= -3.5e-244:
		tmp = t_1
	elif x <= 1.2e-196:
		tmp = y * z
	elif x <= 2e-33:
		tmp = t * a
	elif x <= 2.6e+103:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (x <= -6.8e+56)
		tmp = x;
	elseif (x <= -4.3e-109)
		tmp = Float64(t * a);
	elseif (x <= -3.5e-244)
		tmp = t_1;
	elseif (x <= 1.2e-196)
		tmp = Float64(y * z);
	elseif (x <= 2e-33)
		tmp = Float64(t * a);
	elseif (x <= 2.6e+103)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (x <= -6.8e+56)
		tmp = x;
	elseif (x <= -4.3e-109)
		tmp = t * a;
	elseif (x <= -3.5e-244)
		tmp = t_1;
	elseif (x <= 1.2e-196)
		tmp = y * z;
	elseif (x <= 2e-33)
		tmp = t * a;
	elseif (x <= 2.6e+103)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+56], x, If[LessEqual[x, -4.3e-109], N[(t * a), $MachinePrecision], If[LessEqual[x, -3.5e-244], t$95$1, If[LessEqual[x, 1.2e-196], N[(y * z), $MachinePrecision], If[LessEqual[x, 2e-33], N[(t * a), $MachinePrecision], If[LessEqual[x, 2.6e+103], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.80000000000000002e56 or 2.6000000000000002e103 < x

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 66.1%

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

   if -6.80000000000000002e56 < x < -4.2999999999999997e-109 or 1.2000000000000001e-196 < x < 2.0000000000000001e-33

   1. Initial program 92.0%

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

   3. Taylor expanded in t around inf 49.9%

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

   if -4.2999999999999997e-109 < x < -3.49999999999999992e-244 or 2.0000000000000001e-33 < x < 2.6000000000000002e103

   1. Initial program 88.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 88.3%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)} \]

      2. associate-*r* 88.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}} \]

      3. pow2 88.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \color{blue}{{\left(\sqrt[3]{b}\right)}^{2}}\right) \cdot \sqrt[3]{b} \]

   4. Applied egg-rr 88.4%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot {\left(\sqrt[3]{b}\right)}^{2}\right) \cdot \sqrt[3]{b}} \]

   5. Taylor expanded in b around inf 47.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   7. Simplified 47.1%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]

   if -3.49999999999999992e-244 < x < 1.2000000000000001e-196

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 47.5%

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

      1. *-commutative 47.5%

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

   5. Simplified 47.5%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-109}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-244}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-33}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+103}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-78}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-20}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 620000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+108}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.5e+56)
   x
   (if (<= x -7.4e-78)
     (* t a)
     (if (<= x 9.5e-196)
       (* y z)
       (if (<= x 4.9e-20)
         (* t a)
         (if (<= x 620000.0) (* y z) (if (<= x 1.5e+108) (* t a) x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e+56) {
		tmp = x;
	} else if (x <= -7.4e-78) {
		tmp = t * a;
	} else if (x <= 9.5e-196) {
		tmp = y * z;
	} else if (x <= 4.9e-20) {
		tmp = t * a;
	} else if (x <= 620000.0) {
		tmp = y * z;
	} else if (x <= 1.5e+108) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.5d+56)) then
        tmp = x
    else if (x <= (-7.4d-78)) then
        tmp = t * a
    else if (x <= 9.5d-196) then
        tmp = y * z
    else if (x <= 4.9d-20) then
        tmp = t * a
    else if (x <= 620000.0d0) then
        tmp = y * z
    else if (x <= 1.5d+108) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e+56) {
		tmp = x;
	} else if (x <= -7.4e-78) {
		tmp = t * a;
	} else if (x <= 9.5e-196) {
		tmp = y * z;
	} else if (x <= 4.9e-20) {
		tmp = t * a;
	} else if (x <= 620000.0) {
		tmp = y * z;
	} else if (x <= 1.5e+108) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.5e+56:
		tmp = x
	elif x <= -7.4e-78:
		tmp = t * a
	elif x <= 9.5e-196:
		tmp = y * z
	elif x <= 4.9e-20:
		tmp = t * a
	elif x <= 620000.0:
		tmp = y * z
	elif x <= 1.5e+108:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.5e+56)
		tmp = x;
	elseif (x <= -7.4e-78)
		tmp = Float64(t * a);
	elseif (x <= 9.5e-196)
		tmp = Float64(y * z);
	elseif (x <= 4.9e-20)
		tmp = Float64(t * a);
	elseif (x <= 620000.0)
		tmp = Float64(y * z);
	elseif (x <= 1.5e+108)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.5e+56)
		tmp = x;
	elseif (x <= -7.4e-78)
		tmp = t * a;
	elseif (x <= 9.5e-196)
		tmp = y * z;
	elseif (x <= 4.9e-20)
		tmp = t * a;
	elseif (x <= 620000.0)
		tmp = y * z;
	elseif (x <= 1.5e+108)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.5e+56], x, If[LessEqual[x, -7.4e-78], N[(t * a), $MachinePrecision], If[LessEqual[x, 9.5e-196], N[(y * z), $MachinePrecision], If[LessEqual[x, 4.9e-20], N[(t * a), $MachinePrecision], If[LessEqual[x, 620000.0], N[(y * z), $MachinePrecision], If[LessEqual[x, 1.5e+108], N[(t * a), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5000000000000003e56 or 1.49999999999999992e108 < x

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 66.1%

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

   if -4.5000000000000003e56 < x < -7.40000000000000011e-78 or 9.50000000000000032e-196 < x < 4.9000000000000002e-20 or 6.2e5 < x < 1.49999999999999992e108

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf 46.5%

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

   if -7.40000000000000011e-78 < x < 9.50000000000000032e-196 or 4.9000000000000002e-20 < x < 6.2e5

   1. Initial program 88.5%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. *-commutative 43.6%

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

   5. Simplified 43.6%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-78}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-20}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 620000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+108}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-246}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.5e+53)
   x
   (if (<= x -3.2e-246)
     (* (* z a) b)
     (if (<= x 7.6e-196)
       (* y z)
       (if (<= x 1.55e-32) (* t a) (if (<= x 4.2e+104) (* a (* z b)) x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.5e+53) {
		tmp = x;
	} else if (x <= -3.2e-246) {
		tmp = (z * a) * b;
	} else if (x <= 7.6e-196) {
		tmp = y * z;
	} else if (x <= 1.55e-32) {
		tmp = t * a;
	} else if (x <= 4.2e+104) {
		tmp = a * (z * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.5d+53)) then
        tmp = x
    else if (x <= (-3.2d-246)) then
        tmp = (z * a) * b
    else if (x <= 7.6d-196) then
        tmp = y * z
    else if (x <= 1.55d-32) then
        tmp = t * a
    else if (x <= 4.2d+104) then
        tmp = a * (z * b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.5e+53) {
		tmp = x;
	} else if (x <= -3.2e-246) {
		tmp = (z * a) * b;
	} else if (x <= 7.6e-196) {
		tmp = y * z;
	} else if (x <= 1.55e-32) {
		tmp = t * a;
	} else if (x <= 4.2e+104) {
		tmp = a * (z * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.5e+53:
		tmp = x
	elif x <= -3.2e-246:
		tmp = (z * a) * b
	elif x <= 7.6e-196:
		tmp = y * z
	elif x <= 1.55e-32:
		tmp = t * a
	elif x <= 4.2e+104:
		tmp = a * (z * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.5e+53)
		tmp = x;
	elseif (x <= -3.2e-246)
		tmp = Float64(Float64(z * a) * b);
	elseif (x <= 7.6e-196)
		tmp = Float64(y * z);
	elseif (x <= 1.55e-32)
		tmp = Float64(t * a);
	elseif (x <= 4.2e+104)
		tmp = Float64(a * Float64(z * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.5e+53)
		tmp = x;
	elseif (x <= -3.2e-246)
		tmp = (z * a) * b;
	elseif (x <= 7.6e-196)
		tmp = y * z;
	elseif (x <= 1.55e-32)
		tmp = t * a;
	elseif (x <= 4.2e+104)
		tmp = a * (z * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.5e+53], x, If[LessEqual[x, -3.2e-246], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 7.6e-196], N[(y * z), $MachinePrecision], If[LessEqual[x, 1.55e-32], N[(t * a), $MachinePrecision], If[LessEqual[x, 4.2e+104], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.49999999999999999e53 or 4.1999999999999997e104 < x

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf 65.8%

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

   if -1.49999999999999999e53 < x < -3.2000000000000001e-246

   1. Initial program 92.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 92.3%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)} \]

      2. associate-*r* 92.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}} \]

      3. pow2 92.4%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \color{blue}{{\left(\sqrt[3]{b}\right)}^{2}}\right) \cdot \sqrt[3]{b} \]

   4. Applied egg-rr 92.4%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot {\left(\sqrt[3]{b}\right)}^{2}\right) \cdot \sqrt[3]{b}} \]

   5. Taylor expanded in b around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 37.5%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   7. Simplified 37.5%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.1%

         \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot b} \]

   9. Applied egg-rr 46.1%

      \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot b} \]

   if -3.2000000000000001e-246 < x < 7.6000000000000003e-196

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 47.5%

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

      1. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   if 7.6000000000000003e-196 < x < 1.55000000000000005e-32

   1. Initial program 91.2%

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

   3. Taylor expanded in t around inf 52.8%

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

   if 1.55000000000000005e-32 < x < 4.1999999999999997e104

   1. Initial program 85.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 85.1%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)} \]

      2. associate-*r* 85.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}} \]

      3. pow2 85.0%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \color{blue}{{\left(\sqrt[3]{b}\right)}^{2}}\right) \cdot \sqrt[3]{b} \]

   4. Applied egg-rr 85.0%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot {\left(\sqrt[3]{b}\right)}^{2}\right) \cdot \sqrt[3]{b}} \]

   5. Taylor expanded in b around inf 44.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   7. Simplified 44.5%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-246}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-196}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-32}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+33}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+95} \lor \neg \left(a \leq 3.1 \cdot 10^{+160}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -1.5e+64)
     t_1
     (if (<= a 4.1e+33)
       (+ x (* y z))
       (if (or (<= a 1.05e+95) (not (<= a 3.1e+160))) t_1 (+ x (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.5e+64) {
		tmp = t_1;
	} else if (a <= 4.1e+33) {
		tmp = x + (y * z);
	} else if ((a <= 1.05e+95) || !(a <= 3.1e+160)) {
		tmp = t_1;
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    if (a <= (-1.5d+64)) then
        tmp = t_1
    else if (a <= 4.1d+33) then
        tmp = x + (y * z)
    else if ((a <= 1.05d+95) .or. (.not. (a <= 3.1d+160))) then
        tmp = t_1
    else
        tmp = x + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.5e+64) {
		tmp = t_1;
	} else if (a <= 4.1e+33) {
		tmp = x + (y * z);
	} else if ((a <= 1.05e+95) || !(a <= 3.1e+160)) {
		tmp = t_1;
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -1.5e+64:
		tmp = t_1
	elif a <= 4.1e+33:
		tmp = x + (y * z)
	elif (a <= 1.05e+95) or not (a <= 3.1e+160):
		tmp = t_1
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -1.5e+64)
		tmp = t_1;
	elseif (a <= 4.1e+33)
		tmp = Float64(x + Float64(y * z));
	elseif ((a <= 1.05e+95) || !(a <= 3.1e+160))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -1.5e+64)
		tmp = t_1;
	elseif (a <= 4.1e+33)
		tmp = x + (y * z);
	elseif ((a <= 1.05e+95) || ~((a <= 3.1e+160)))
		tmp = t_1;
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+64], t$95$1, If[LessEqual[a, 4.1e+33], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.05e+95], N[Not[LessEqual[a, 3.1e+160]], $MachinePrecision]], t$95$1, N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5000000000000001e64 or 4.09999999999999995e33 < a < 1.05e95 or 3.0999999999999998e160 < a

   1. Initial program 79.3%

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

   3. Taylor expanded in a around inf 84.4%

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

   if -1.5000000000000001e64 < a < 4.09999999999999995e33

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0 75.8%

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

   if 1.05e95 < a < 3.0999999999999998e160

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 79.5%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+33}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+95} \lor \neg \left(a \leq 3.1 \cdot 10^{+160}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+20} \lor \neg \left(b \leq 3.2 \cdot 10^{+72}\right):\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.6e+20) (not (<= b 3.2e+72)))
   (+ x (+ (* t a) (* a (* z b))))
   (+ x (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+20) || !(b <= 3.2e+72)) {
		tmp = x + ((t * a) + (a * (z * b)));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.6d+20)) .or. (.not. (b <= 3.2d+72))) then
        tmp = x + ((t * a) + (a * (z * b)))
    else
        tmp = x + ((t * a) + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+20) || !(b <= 3.2e+72)) {
		tmp = x + ((t * a) + (a * (z * b)));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.6e+20) or not (b <= 3.2e+72):
		tmp = x + ((t * a) + (a * (z * b)))
	else:
		tmp = x + ((t * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.6e+20) || !(b <= 3.2e+72))
		tmp = Float64(x + Float64(Float64(t * a) + Float64(a * Float64(z * b))));
	else
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.6e+20) || ~((b <= 3.2e+72)))
		tmp = x + ((t * a) + (a * (z * b)));
	else
		tmp = x + ((t * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.6e+20], N[Not[LessEqual[b, 3.2e+72]], $MachinePrecision]], N[(x + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.6e20 or 3.2000000000000001e72 < b

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0 80.0%

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

   if -3.6e20 < b < 3.2000000000000001e72

   1. Initial program 89.8%

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

   3. Taylor expanded in b around 0 92.8%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+20} \lor \neg \left(b \leq 3.2 \cdot 10^{+72}\right):\\ \;\;\;\;x + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+232}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+82}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.2e+232)
   (* (* z a) b)
   (if (<= b 7.5e+82) (+ x (+ (* t a) (* y z))) (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+232) {
		tmp = (z * a) * b;
	} else if (b <= 7.5e+82) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.2d+232)) then
        tmp = (z * a) * b
    else if (b <= 7.5d+82) then
        tmp = x + ((t * a) + (y * z))
    else
        tmp = a * (t + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+232) {
		tmp = (z * a) * b;
	} else if (b <= 7.5e+82) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = a * (t + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.2e+232:
		tmp = (z * a) * b
	elif b <= 7.5e+82:
		tmp = x + ((t * a) + (y * z))
	else:
		tmp = a * (t + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.2e+232)
		tmp = Float64(Float64(z * a) * b);
	elseif (b <= 7.5e+82)
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	else
		tmp = Float64(a * Float64(t + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.2e+232)
		tmp = (z * a) * b;
	elseif (b <= 7.5e+82)
		tmp = x + ((t * a) + (y * z));
	else
		tmp = a * (t + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.2e+232], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 7.5e+82], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2e232

   1. Initial program 81.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 80.6%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)} \]

      2. associate-*r* 80.8%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}} \]

      3. pow2 80.8%

         \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \color{blue}{{\left(\sqrt[3]{b}\right)}^{2}}\right) \cdot \sqrt[3]{b} \]

   4. Applied egg-rr 80.8%

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(a \cdot z\right) \cdot {\left(\sqrt[3]{b}\right)}^{2}\right) \cdot \sqrt[3]{b}} \]

   5. Taylor expanded in b around inf 58.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 58.5%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   7. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 76.1%

         \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot b} \]

   9. Applied egg-rr 76.1%

      \[\leadsto \color{blue}{\left(a \cdot z\right) \cdot b} \]

   if -2.2e232 < b < 7.4999999999999999e82

   1. Initial program 90.4%

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

   3. Taylor expanded in b around 0 87.3%

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

   if 7.4999999999999999e82 < b

   1. Initial program 88.6%

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

   3. Taylor expanded in a around inf 78.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+232}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+82}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+66} \lor \neg \left(z \leq 1.3 \cdot 10^{-27}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7e+66) (not (<= z 1.3e-27)))
   (* z (+ y (* a b)))
   (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e+66) || !(z <= 1.3e-27)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7d+66)) .or. (.not. (z <= 1.3d-27))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e+66) || !(z <= 1.3e-27)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7e+66) or not (z <= 1.3e-27):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7e+66) || !(z <= 1.3e-27))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7e+66) || ~((z <= 1.3e-27)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7e+66], N[Not[LessEqual[z, 1.3e-27]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999994e66 or 1.30000000000000009e-27 < z

   1. Initial program 79.3%

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

   3. Taylor expanded in z around inf 77.5%

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

   if -6.9999999999999994e66 < z < 1.30000000000000009e-27

   1. Initial program 97.9%

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

   3. Taylor expanded in z around 0 79.1%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+66} \lor \neg \left(z \leq 1.3 \cdot 10^{-27}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.75e+68)
   (* z (* a b))
   (if (<= z 1.35e+62) (+ x (* t a)) (+ x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.75e+68) {
		tmp = z * (a * b);
	} else if (z <= 1.35e+62) {
		tmp = x + (t * a);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.75d+68)) then
        tmp = z * (a * b)
    else if (z <= 1.35d+62) then
        tmp = x + (t * a)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.75e+68) {
		tmp = z * (a * b);
	} else if (z <= 1.35e+62) {
		tmp = x + (t * a);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.75e+68:
		tmp = z * (a * b)
	elif z <= 1.35e+62:
		tmp = x + (t * a)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.75e+68)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 1.35e+62)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.75e+68)
		tmp = z * (a * b);
	elseif (z <= 1.35e+62)
		tmp = x + (t * a);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.75e+68], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+62], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.74999999999999989e68

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf 82.3%

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

   4. Taylor expanded in y around 0 54.3%

      \[\leadsto z \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -1.74999999999999989e68 < z < 1.35e62

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 74.9%

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

   if 1.35e62 < z

   1. Initial program 80.8%

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

   3. Taylor expanded in a around 0 65.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+132}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.5e+68) (* z (* a b)) (if (<= z 1.1e+132) (+ x (* t a)) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.5e+68) {
		tmp = z * (a * b);
	} else if (z <= 1.1e+132) {
		tmp = x + (t * a);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.5d+68)) then
        tmp = z * (a * b)
    else if (z <= 1.1d+132) then
        tmp = x + (t * a)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.5e+68) {
		tmp = z * (a * b);
	} else if (z <= 1.1e+132) {
		tmp = x + (t * a);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.5e+68:
		tmp = z * (a * b)
	elif z <= 1.1e+132:
		tmp = x + (t * a)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.5e+68)
		tmp = Float64(z * Float64(a * b));
	elseif (z <= 1.1e+132)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.5e+68)
		tmp = z * (a * b);
	elseif (z <= 1.1e+132)
		tmp = x + (t * a);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.5e+68], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+132], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5000000000000003e68

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf 82.3%

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

   4. Taylor expanded in y around 0 54.3%

      \[\leadsto z \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -4.5000000000000003e68 < z < 1.09999999999999994e132

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 72.6%

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

   if 1.09999999999999994e132 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in y around inf 59.8%

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

      1. *-commutative 59.8%

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

   5. Simplified 59.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+132}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+56} \lor \neg \left(x \leq 4.6 \cdot 10^{+103}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -5.8e+56) (not (<= x 4.6e+103))) x (* t a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5.8e+56) || !(x <= 4.6e+103)) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x <= (-5.8d+56)) .or. (.not. (x <= 4.6d+103))) then
        tmp = x
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -5.8e+56) || !(x <= 4.6e+103)) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -5.8e+56) or not (x <= 4.6e+103):
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -5.8e+56) || !(x <= 4.6e+103))
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -5.8e+56) || ~((x <= 4.6e+103)))
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -5.8e+56], N[Not[LessEqual[x, 4.6e+103]], $MachinePrecision]], x, N[(t * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.80000000000000014e56 or 4.60000000000000017e103 < x

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 66.1%

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

   if -5.80000000000000014e56 < x < 4.60000000000000017e103

   1. Initial program 89.6%

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

   3. Taylor expanded in t around inf 35.4%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+56} \lor \neg \left(x \leq 4.6 \cdot 10^{+103}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.4% accurate, 15.0× speedup

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 89.5%

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

3. Taylor expanded in x around inf 30.0%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 97.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))