Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 99.1%

Time: 10.9s

Alternatives: 13

Speedup: 0.6×

• 32.3% 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: 92.5% 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: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+59} \lor \neg \left(z \leq 8.2 \cdot 10^{+35}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot t + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5e+59) (not (<= z 8.2e+35)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ (+ x (* z y)) (+ (* a t) (* a (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5e+59) || !(z <= 8.2e+35)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = (x + (z * y)) + ((a * t) + (a * (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 ((z <= (-5d+59)) .or. (.not. (z <= 8.2d+35))) then
        tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
    else
        tmp = (x + (z * y)) + ((a * t) + (a * (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 ((z <= -5e+59) || !(z <= 8.2e+35)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = (x + (z * y)) + ((a * t) + (a * (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5e+59) or not (z <= 8.2e+35):
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	else:
		tmp = (x + (z * y)) + ((a * t) + (a * (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5e+59) || !(z <= 8.2e+35))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	else
		tmp = Float64(Float64(x + Float64(z * y)) + Float64(Float64(a * t) + Float64(a * Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5e+59) || ~((z <= 8.2e+35)))
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	else
		tmp = (x + (z * y)) + ((a * t) + (a * (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5e+59], N[Not[LessEqual[z, 8.2e+35]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999997e59 or 8.1999999999999997e35 < z

   1. Initial program 82.5%

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

      1. associate-+l+ 82.5%

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

      2. associate-*l* 73.6%

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

   3. Simplified 73.6%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-+l+ 93.8%

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

      3. +-commutative 93.8%

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

      4. associate-/l* 98.1%

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

      5. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   if -4.9999999999999997e59 < z < 8.1999999999999997e35

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+59} \lor \neg \left(z \leq 8.2 \cdot 10^{+35}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot t + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 38.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot a\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-293}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+36}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+275}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (* z a))))
   (if (<= z -1.05e+23)
     t_1
     (if (<= z -1.1e-173)
       x
       (if (<= z -2.9e-293)
         (* a t)
         (if (<= z 1.82e-115)
           x
           (if (<= z 4.3e+36) (* a t) (if (<= z 1.2e+275) t_1 (* z y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (z * a);
	double tmp;
	if (z <= -1.05e+23) {
		tmp = t_1;
	} else if (z <= -1.1e-173) {
		tmp = x;
	} else if (z <= -2.9e-293) {
		tmp = a * t;
	} else if (z <= 1.82e-115) {
		tmp = x;
	} else if (z <= 4.3e+36) {
		tmp = a * t;
	} else if (z <= 1.2e+275) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	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 = b * (z * a)
    if (z <= (-1.05d+23)) then
        tmp = t_1
    else if (z <= (-1.1d-173)) then
        tmp = x
    else if (z <= (-2.9d-293)) then
        tmp = a * t
    else if (z <= 1.82d-115) then
        tmp = x
    else if (z <= 4.3d+36) then
        tmp = a * t
    else if (z <= 1.2d+275) then
        tmp = t_1
    else
        tmp = z * y
    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 = b * (z * a);
	double tmp;
	if (z <= -1.05e+23) {
		tmp = t_1;
	} else if (z <= -1.1e-173) {
		tmp = x;
	} else if (z <= -2.9e-293) {
		tmp = a * t;
	} else if (z <= 1.82e-115) {
		tmp = x;
	} else if (z <= 4.3e+36) {
		tmp = a * t;
	} else if (z <= 1.2e+275) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (z * a)
	tmp = 0
	if z <= -1.05e+23:
		tmp = t_1
	elif z <= -1.1e-173:
		tmp = x
	elif z <= -2.9e-293:
		tmp = a * t
	elif z <= 1.82e-115:
		tmp = x
	elif z <= 4.3e+36:
		tmp = a * t
	elif z <= 1.2e+275:
		tmp = t_1
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(z * a))
	tmp = 0.0
	if (z <= -1.05e+23)
		tmp = t_1;
	elseif (z <= -1.1e-173)
		tmp = x;
	elseif (z <= -2.9e-293)
		tmp = Float64(a * t);
	elseif (z <= 1.82e-115)
		tmp = x;
	elseif (z <= 4.3e+36)
		tmp = Float64(a * t);
	elseif (z <= 1.2e+275)
		tmp = t_1;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (z * a);
	tmp = 0.0;
	if (z <= -1.05e+23)
		tmp = t_1;
	elseif (z <= -1.1e-173)
		tmp = x;
	elseif (z <= -2.9e-293)
		tmp = a * t;
	elseif (z <= 1.82e-115)
		tmp = x;
	elseif (z <= 4.3e+36)
		tmp = a * t;
	elseif (z <= 1.2e+275)
		tmp = t_1;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+23], t$95$1, If[LessEqual[z, -1.1e-173], x, If[LessEqual[z, -2.9e-293], N[(a * t), $MachinePrecision], If[LessEqual[z, 1.82e-115], x, If[LessEqual[z, 4.3e+36], N[(a * t), $MachinePrecision], If[LessEqual[z, 1.2e+275], t$95$1, N[(z * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0500000000000001e23 or 4.30000000000000005e36 < z < 1.19999999999999998e275

   1. Initial program 83.0%

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

      1. associate-+l+ 83.0%

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

      2. associate-*l* 74.7%

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

   3. Simplified 74.7%

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

      1. add-cube-cbrt 74.5%

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

      2. pow3 74.6%

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

   6. Applied egg-rr 74.6%

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

   7. Taylor expanded in b around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. associate-*r* 53.1%

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

   9. Simplified 53.1%

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

   if -1.0500000000000001e23 < z < -1.1e-173 or -2.8999999999999999e-293 < z < 1.82000000000000003e-115

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 49.4%

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

   if -1.1e-173 < z < -2.8999999999999999e-293 or 1.82000000000000003e-115 < z < 4.30000000000000005e36

   1. Initial program 98.2%

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

      1. associate-+l+ 98.2%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 53.2%

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

   if 1.19999999999999998e275 < z

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 71.4%

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

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.3%

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

      1. *-commutative 86.3%

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

   7. Simplified 86.3%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-293}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+36}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+275}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-182}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-297}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+39}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+275}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* a b))))
   (if (<= z -1.8e+22)
     t_1
     (if (<= z -4.2e-182)
       x
       (if (<= z -3.5e-297)
         (* a t)
         (if (<= z 3.1e-118)
           x
           (if (<= z 3.3e+39) (* a t) (if (<= z 5.5e+275) t_1 (* z y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a * b);
	double tmp;
	if (z <= -1.8e+22) {
		tmp = t_1;
	} else if (z <= -4.2e-182) {
		tmp = x;
	} else if (z <= -3.5e-297) {
		tmp = a * t;
	} else if (z <= 3.1e-118) {
		tmp = x;
	} else if (z <= 3.3e+39) {
		tmp = a * t;
	} else if (z <= 5.5e+275) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	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 * (a * b)
    if (z <= (-1.8d+22)) then
        tmp = t_1
    else if (z <= (-4.2d-182)) then
        tmp = x
    else if (z <= (-3.5d-297)) then
        tmp = a * t
    else if (z <= 3.1d-118) then
        tmp = x
    else if (z <= 3.3d+39) then
        tmp = a * t
    else if (z <= 5.5d+275) then
        tmp = t_1
    else
        tmp = z * y
    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 * (a * b);
	double tmp;
	if (z <= -1.8e+22) {
		tmp = t_1;
	} else if (z <= -4.2e-182) {
		tmp = x;
	} else if (z <= -3.5e-297) {
		tmp = a * t;
	} else if (z <= 3.1e-118) {
		tmp = x;
	} else if (z <= 3.3e+39) {
		tmp = a * t;
	} else if (z <= 5.5e+275) {
		tmp = t_1;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a * b)
	tmp = 0
	if z <= -1.8e+22:
		tmp = t_1
	elif z <= -4.2e-182:
		tmp = x
	elif z <= -3.5e-297:
		tmp = a * t
	elif z <= 3.1e-118:
		tmp = x
	elif z <= 3.3e+39:
		tmp = a * t
	elif z <= 5.5e+275:
		tmp = t_1
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a * b))
	tmp = 0.0
	if (z <= -1.8e+22)
		tmp = t_1;
	elseif (z <= -4.2e-182)
		tmp = x;
	elseif (z <= -3.5e-297)
		tmp = Float64(a * t);
	elseif (z <= 3.1e-118)
		tmp = x;
	elseif (z <= 3.3e+39)
		tmp = Float64(a * t);
	elseif (z <= 5.5e+275)
		tmp = t_1;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a * b);
	tmp = 0.0;
	if (z <= -1.8e+22)
		tmp = t_1;
	elseif (z <= -4.2e-182)
		tmp = x;
	elseif (z <= -3.5e-297)
		tmp = a * t;
	elseif (z <= 3.1e-118)
		tmp = x;
	elseif (z <= 3.3e+39)
		tmp = a * t;
	elseif (z <= 5.5e+275)
		tmp = t_1;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+22], t$95$1, If[LessEqual[z, -4.2e-182], x, If[LessEqual[z, -3.5e-297], N[(a * t), $MachinePrecision], If[LessEqual[z, 3.1e-118], x, If[LessEqual[z, 3.3e+39], N[(a * t), $MachinePrecision], If[LessEqual[z, 5.5e+275], t$95$1, N[(z * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e22 or 3.30000000000000021e39 < z < 5.5000000000000002e275

   1. Initial program 83.0%

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

      1. associate-+l+ 83.0%

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

      2. associate-*l* 74.7%

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

   3. Simplified 74.7%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.4%

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

   6. Taylor expanded in y around 0 52.2%

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

   if -1.8e22 < z < -4.2000000000000001e-182 or -3.4999999999999999e-297 < z < 3.1000000000000001e-118

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 49.4%

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

   if -4.2000000000000001e-182 < z < -3.4999999999999999e-297 or 3.1000000000000001e-118 < z < 3.30000000000000021e39

   1. Initial program 98.2%

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

      1. associate-+l+ 98.2%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 53.2%

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

   if 5.5000000000000002e275 < z

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 71.4%

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

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.3%

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

      1. *-commutative 86.3%

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

   7. Simplified 86.3%

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

Alternative 4: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+158} \lor \neg \left(z \leq -1.9 \cdot 10^{+71}\right) \land \left(z \leq -3400000000 \lor \neg \left(z \leq 2 \cdot 10^{+61}\right)\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.2e+158)
         (and (not (<= z -1.9e+71))
              (or (<= z -3400000000.0) (not (<= z 2e+61)))))
   (* z (+ y (* a b)))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.2e+158) || (!(z <= -1.9e+71) && ((z <= -3400000000.0) || !(z <= 2e+61)))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (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 ((z <= (-2.2d+158)) .or. (.not. (z <= (-1.9d+71))) .and. (z <= (-3400000000.0d0)) .or. (.not. (z <= 2d+61))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (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 ((z <= -2.2e+158) || (!(z <= -1.9e+71) && ((z <= -3400000000.0) || !(z <= 2e+61)))) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.2e+158) or (not (z <= -1.9e+71) and ((z <= -3400000000.0) or not (z <= 2e+61))):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.2e+158) || (!(z <= -1.9e+71) && ((z <= -3400000000.0) || !(z <= 2e+61))))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + 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 ((z <= -2.2e+158) || (~((z <= -1.9e+71)) && ((z <= -3400000000.0) || ~((z <= 2e+61)))))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.2e+158], And[N[Not[LessEqual[z, -1.9e+71]], $MachinePrecision], Or[LessEqual[z, -3400000000.0], N[Not[LessEqual[z, 2e+61]], $MachinePrecision]]]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e158 or -1.9e71 < z < -3.4e9 or 1.9999999999999999e61 < z

   1. Initial program 84.4%

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

      1. associate-+l+ 84.4%

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

      2. associate-*l* 73.4%

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

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 90.8%

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

   if -2.2000000000000001e158 < z < -1.9e71 or -3.4e9 < z < 1.9999999999999999e61

   1. Initial program 97.1%

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

      1. associate-+l+ 97.1%

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

      2. +-commutative 97.1%

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

      3. fma-define 97.2%

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

      4. associate-*l* 98.0%

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

      5. *-commutative 98.0%

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

      6. *-commutative 98.0%

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

      7. distribute-rgt-out 98.7%

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

      8. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 93.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+158} \lor \neg \left(z \leq -1.9 \cdot 10^{+71}\right) \land \left(z \leq -3400000000 \lor \neg \left(z \leq 2 \cdot 10^{+61}\right)\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{+81}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= t -6.1e+81)
     (* a t)
     (if (<= t -1.15e-46)
       t_1
       (if (<= t -2.5e-217)
         x
         (if (<= t 1.65e-70) t_1 (if (<= t 6.8e+81) x (* a t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (t <= -6.1e+81) {
		tmp = a * t;
	} else if (t <= -1.15e-46) {
		tmp = t_1;
	} else if (t <= -2.5e-217) {
		tmp = x;
	} else if (t <= 1.65e-70) {
		tmp = t_1;
	} else if (t <= 6.8e+81) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	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 (t <= (-6.1d+81)) then
        tmp = a * t
    else if (t <= (-1.15d-46)) then
        tmp = t_1
    else if (t <= (-2.5d-217)) then
        tmp = x
    else if (t <= 1.65d-70) then
        tmp = t_1
    else if (t <= 6.8d+81) then
        tmp = x
    else
        tmp = a * t
    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 (t <= -6.1e+81) {
		tmp = a * t;
	} else if (t <= -1.15e-46) {
		tmp = t_1;
	} else if (t <= -2.5e-217) {
		tmp = x;
	} else if (t <= 1.65e-70) {
		tmp = t_1;
	} else if (t <= 6.8e+81) {
		tmp = x;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if t <= -6.1e+81:
		tmp = a * t
	elif t <= -1.15e-46:
		tmp = t_1
	elif t <= -2.5e-217:
		tmp = x
	elif t <= 1.65e-70:
		tmp = t_1
	elif t <= 6.8e+81:
		tmp = x
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (t <= -6.1e+81)
		tmp = Float64(a * t);
	elseif (t <= -1.15e-46)
		tmp = t_1;
	elseif (t <= -2.5e-217)
		tmp = x;
	elseif (t <= 1.65e-70)
		tmp = t_1;
	elseif (t <= 6.8e+81)
		tmp = x;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (t <= -6.1e+81)
		tmp = a * t;
	elseif (t <= -1.15e-46)
		tmp = t_1;
	elseif (t <= -2.5e-217)
		tmp = x;
	elseif (t <= 1.65e-70)
		tmp = t_1;
	elseif (t <= 6.8e+81)
		tmp = x;
	else
		tmp = a * t;
	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[t, -6.1e+81], N[(a * t), $MachinePrecision], If[LessEqual[t, -1.15e-46], t$95$1, If[LessEqual[t, -2.5e-217], x, If[LessEqual[t, 1.65e-70], t$95$1, If[LessEqual[t, 6.8e+81], x, N[(a * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.10000000000000038e81 or 6.80000000000000005e81 < t

   1. Initial program 92.8%

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

      1. associate-+l+ 92.8%

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

      2. associate-*l* 86.0%

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

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 56.4%

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

   if -6.10000000000000038e81 < t < -1.15e-46 or -2.5000000000000001e-217 < t < 1.65000000000000008e-70

   1. Initial program 92.2%

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

      1. associate-+l+ 92.2%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

      1. add-cube-cbrt 89.0%

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

      2. pow3 89.1%

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

   6. Applied egg-rr 89.1%

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

   7. Taylor expanded in b around inf 43.3%

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

   if -1.15e-46 < t < -2.5000000000000001e-217 or 1.65000000000000008e-70 < t < 6.80000000000000005e81

   1. Initial program 91.0%

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

      1. associate-+l+ 91.0%

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

      2. associate-*l* 89.0%

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

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 47.3%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+81}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-292}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+60}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.7)
   (* z y)
   (if (<= z -3e-183)
     x
     (if (<= z -2.9e-292)
       (* a t)
       (if (<= z 8.5e-117) x (if (<= z 2.3e+60) (* a t) (* z y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.7) {
		tmp = z * y;
	} else if (z <= -3e-183) {
		tmp = x;
	} else if (z <= -2.9e-292) {
		tmp = a * t;
	} else if (z <= 8.5e-117) {
		tmp = x;
	} else if (z <= 2.3e+60) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	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 <= (-1.7d0)) then
        tmp = z * y
    else if (z <= (-3d-183)) then
        tmp = x
    else if (z <= (-2.9d-292)) then
        tmp = a * t
    else if (z <= 8.5d-117) then
        tmp = x
    else if (z <= 2.3d+60) then
        tmp = a * t
    else
        tmp = z * y
    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 <= -1.7) {
		tmp = z * y;
	} else if (z <= -3e-183) {
		tmp = x;
	} else if (z <= -2.9e-292) {
		tmp = a * t;
	} else if (z <= 8.5e-117) {
		tmp = x;
	} else if (z <= 2.3e+60) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.7:
		tmp = z * y
	elif z <= -3e-183:
		tmp = x
	elif z <= -2.9e-292:
		tmp = a * t
	elif z <= 8.5e-117:
		tmp = x
	elif z <= 2.3e+60:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.7)
		tmp = Float64(z * y);
	elseif (z <= -3e-183)
		tmp = x;
	elseif (z <= -2.9e-292)
		tmp = Float64(a * t);
	elseif (z <= 8.5e-117)
		tmp = x;
	elseif (z <= 2.3e+60)
		tmp = Float64(a * t);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.7)
		tmp = z * y;
	elseif (z <= -3e-183)
		tmp = x;
	elseif (z <= -2.9e-292)
		tmp = a * t;
	elseif (z <= 8.5e-117)
		tmp = x;
	elseif (z <= 2.3e+60)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.7], N[(z * y), $MachinePrecision], If[LessEqual[z, -3e-183], x, If[LessEqual[z, -2.9e-292], N[(a * t), $MachinePrecision], If[LessEqual[z, 8.5e-117], x, If[LessEqual[z, 2.3e+60], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999996 or 2.30000000000000017e60 < z

   1. Initial program 84.4%

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

      1. associate-+l+ 84.4%

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

      2. associate-*l* 75.2%

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

   3. Simplified 75.2%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 44.0%

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

      1. *-commutative 44.0%

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

   7. Simplified 44.0%

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

   if -1.69999999999999996 < z < -2.9999999999999998e-183 or -2.89999999999999993e-292 < z < 8.49999999999999981e-117

   1. Initial program 99.5%

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

      1. associate-+l+ 99.5%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 51.8%

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

   if -2.9999999999999998e-183 < z < -2.89999999999999993e-292 or 8.49999999999999981e-117 < z < 2.30000000000000017e60

   1. Initial program 98.3%

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

      1. associate-+l+ 98.3%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 52.2%

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

Alternative 7: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot y\\ t_2 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+95}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z y))) (t_2 (* a (+ t (* z b)))))
   (if (<= a -4.6e-34)
     t_2
     (if (<= a 1e-17)
       t_1
       (if (<= a 8.6e+95) (+ x (* a t)) (if (<= a 1.6e+131) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -4.6e-34) {
		tmp = t_2;
	} else if (a <= 1e-17) {
		tmp = t_1;
	} else if (a <= 8.6e+95) {
		tmp = x + (a * t);
	} else if (a <= 1.6e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + (z * y)
    t_2 = a * (t + (z * b))
    if (a <= (-4.6d-34)) then
        tmp = t_2
    else if (a <= 1d-17) then
        tmp = t_1
    else if (a <= 8.6d+95) then
        tmp = x + (a * t)
    else if (a <= 1.6d+131) 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 a, double b) {
	double t_1 = x + (z * y);
	double t_2 = a * (t + (z * b));
	double tmp;
	if (a <= -4.6e-34) {
		tmp = t_2;
	} else if (a <= 1e-17) {
		tmp = t_1;
	} else if (a <= 8.6e+95) {
		tmp = x + (a * t);
	} else if (a <= 1.6e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * y)
	t_2 = a * (t + (z * b))
	tmp = 0
	if a <= -4.6e-34:
		tmp = t_2
	elif a <= 1e-17:
		tmp = t_1
	elif a <= 8.6e+95:
		tmp = x + (a * t)
	elif a <= 1.6e+131:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * y))
	t_2 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -4.6e-34)
		tmp = t_2;
	elseif (a <= 1e-17)
		tmp = t_1;
	elseif (a <= 8.6e+95)
		tmp = Float64(x + Float64(a * t));
	elseif (a <= 1.6e+131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * y);
	t_2 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -4.6e-34)
		tmp = t_2;
	elseif (a <= 1e-17)
		tmp = t_1;
	elseif (a <= 8.6e+95)
		tmp = x + (a * t);
	elseif (a <= 1.6e+131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e-34], t$95$2, If[LessEqual[a, 1e-17], t$95$1, If[LessEqual[a, 8.6e+95], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+131], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.60000000000000022e-34 or 1.6000000000000001e131 < a

   1. Initial program 83.7%

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

      1. associate-+l+ 83.7%

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

      2. associate-*l* 89.9%

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

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 80.7%

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

   if -4.60000000000000022e-34 < a < 1.00000000000000007e-17 or 8.6e95 < a < 1.6000000000000001e131

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. associate-*l* 85.0%

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

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 71.1%

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

   if 1.00000000000000007e-17 < a < 8.6e95

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 74.9%

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

      1. +-commutative 74.9%

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

   7. Simplified 74.9%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 10^{-17}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+95}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+131}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot y\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -3400000000 \lor \neg \left(z \leq 1.55 \cdot 10^{+60}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z y))))
   (if (<= z -2.7e+226)
     t_1
     (if (<= z -1e+121)
       (* z (* a b))
       (if (or (<= z -3400000000.0) (not (<= z 1.55e+60)))
         t_1
         (+ x (* a t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * y);
	double tmp;
	if (z <= -2.7e+226) {
		tmp = t_1;
	} else if (z <= -1e+121) {
		tmp = z * (a * b);
	} else if ((z <= -3400000000.0) || !(z <= 1.55e+60)) {
		tmp = t_1;
	} else {
		tmp = x + (a * t);
	}
	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 = x + (z * y)
    if (z <= (-2.7d+226)) then
        tmp = t_1
    else if (z <= (-1d+121)) then
        tmp = z * (a * b)
    else if ((z <= (-3400000000.0d0)) .or. (.not. (z <= 1.55d+60))) then
        tmp = t_1
    else
        tmp = x + (a * t)
    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 = x + (z * y);
	double tmp;
	if (z <= -2.7e+226) {
		tmp = t_1;
	} else if (z <= -1e+121) {
		tmp = z * (a * b);
	} else if ((z <= -3400000000.0) || !(z <= 1.55e+60)) {
		tmp = t_1;
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * y)
	tmp = 0
	if z <= -2.7e+226:
		tmp = t_1
	elif z <= -1e+121:
		tmp = z * (a * b)
	elif (z <= -3400000000.0) or not (z <= 1.55e+60):
		tmp = t_1
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * y))
	tmp = 0.0
	if (z <= -2.7e+226)
		tmp = t_1;
	elseif (z <= -1e+121)
		tmp = Float64(z * Float64(a * b));
	elseif ((z <= -3400000000.0) || !(z <= 1.55e+60))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * y);
	tmp = 0.0;
	if (z <= -2.7e+226)
		tmp = t_1;
	elseif (z <= -1e+121)
		tmp = z * (a * b);
	elseif ((z <= -3400000000.0) || ~((z <= 1.55e+60)))
		tmp = t_1;
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+226], t$95$1, If[LessEqual[z, -1e+121], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3400000000.0], N[Not[LessEqual[z, 1.55e+60]], $MachinePrecision]], t$95$1, N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000003e226 or -1.00000000000000004e121 < z < -3.4e9 or 1.55e60 < z

   1. Initial program 84.3%

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

      1. associate-+l+ 84.3%

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

      2. associate-*l* 77.5%

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

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 59.1%

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

   if -2.7000000000000003e226 < z < -1.00000000000000004e121

   1. Initial program 83.4%

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

      1. associate-+l+ 83.4%

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

      2. associate-*l* 64.0%

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

   3. Simplified 64.0%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 87.2%

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

   6. Taylor expanded in y around 0 70.8%

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

   if -3.4e9 < z < 1.55e60

   1. Initial program 99.0%

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

      1. associate-+l+ 99.0%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 75.9%

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

      1. +-commutative 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+226}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -3400000000 \lor \neg \left(z \leq 1.55 \cdot 10^{+60}\right):\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-74} \lor \neg \left(z \leq 2.8\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.8e-74) (not (<= z 2.8)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.8e-74) || !(z <= 2.8)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = x + (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 ((z <= (-1.8d-74)) .or. (.not. (z <= 2.8d0))) then
        tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
    else
        tmp = x + (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 ((z <= -1.8e-74) || !(z <= 2.8)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.8e-74) or not (z <= 2.8):
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.8e-74) || !(z <= 2.8))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	else
		tmp = Float64(x + 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 ((z <= -1.8e-74) || ~((z <= 2.8)))
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.8e-74], N[Not[LessEqual[z, 2.8]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e-74 or 2.7999999999999998 < z

   1. Initial program 86.5%

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

      1. associate-+l+ 86.5%

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

      2. associate-*l* 79.6%

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

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-+l+ 94.5%

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

      3. +-commutative 94.5%

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

      4. associate-/l* 97.2%

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

      5. distribute-lft-out 98.6%

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

   7. Simplified 98.6%

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

   if -1.8000000000000001e-74 < z < 2.7999999999999998

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. fma-define 99.7%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-rgt-out 99.9%

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

      8. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 97.1%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-74} \lor \neg \left(z \leq 2.8\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4200 \lor \neg \left(z \leq 6.6 \cdot 10^{+44}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4200.0) (not (<= z 6.6e+44)))
   (* z (+ y (* a b)))
   (+ x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4200.0) || !(z <= 6.6e+44)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	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 <= (-4200.0d0)) .or. (.not. (z <= 6.6d+44))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (a * t)
    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 <= -4200.0) || !(z <= 6.6e+44)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4200.0) or not (z <= 6.6e+44):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4200.0) || !(z <= 6.6e+44))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4200.0) || ~((z <= 6.6e+44)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4200.0], N[Not[LessEqual[z, 6.6e+44]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4200 or 6.60000000000000027e44 < z

   1. Initial program 84.6%

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

      1. associate-+l+ 84.6%

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

      2. associate-*l* 75.6%

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

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 85.1%

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

   if -4200 < z < 6.60000000000000027e44

   1. Initial program 99.0%

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

      1. associate-+l+ 99.0%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 77.3%

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

      1. +-commutative 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4200 \lor \neg \left(z \leq 6.6 \cdot 10^{+44}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+16} \lor \neg \left(a \leq 1.65 \cdot 10^{+131}\right):\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5e+16) (not (<= a 1.65e+131))) (* b (* z a)) (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5e+16) || !(a <= 1.65e+131)) {
		tmp = b * (z * a);
	} else {
		tmp = x + (z * y);
	}
	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 ((a <= (-5d+16)) .or. (.not. (a <= 1.65d+131))) then
        tmp = b * (z * a)
    else
        tmp = x + (z * y)
    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 ((a <= -5e+16) || !(a <= 1.65e+131)) {
		tmp = b * (z * a);
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5e+16) or not (a <= 1.65e+131):
		tmp = b * (z * a)
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -5e+16) || !(a <= 1.65e+131))
		tmp = Float64(b * Float64(z * a));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -5e+16) || ~((a <= 1.65e+131)))
		tmp = b * (z * a);
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -5e+16], N[Not[LessEqual[a, 1.65e+131]], $MachinePrecision]], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5e16 or 1.6499999999999999e131 < a

   1. Initial program 81.9%

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

      1. associate-+l+ 81.9%

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

      2. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

      1. add-cube-cbrt 88.4%

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

      2. pow3 88.5%

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

   6. Applied egg-rr 88.5%

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

   7. Taylor expanded in b around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. associate-*r* 54.9%

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

   9. Simplified 54.9%

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

   if -5e16 < a < 1.6499999999999999e131

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 87.9%

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

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 66.7%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+16} \lor \neg \left(a \leq 1.65 \cdot 10^{+131}\right):\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+56} \lor \neg \left(t \leq 6 \cdot 10^{+81}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.55e+56) (not (<= t 6e+81))) (* a t) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.55e+56) || !(t <= 6e+81)) {
		tmp = a * t;
	} 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 ((t <= (-2.55d+56)) .or. (.not. (t <= 6d+81))) then
        tmp = a * t
    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 ((t <= -2.55e+56) || !(t <= 6e+81)) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.55e+56) or not (t <= 6e+81):
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.55e+56) || !(t <= 6e+81))
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.55e+56) || ~((t <= 6e+81)))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.55e+56], N[Not[LessEqual[t, 6e+81]], $MachinePrecision]], N[(a * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.5500000000000001e56 or 5.99999999999999995e81 < t

   1. Initial program 92.3%

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

      1. associate-+l+ 92.3%

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

      2. associate-*l* 87.1%

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

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 54.3%

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

   if -2.5500000000000001e56 < t < 5.99999999999999995e81

   1. Initial program 92.0%

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

      1. associate-+l+ 92.0%

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

      2. associate-*l* 88.8%

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

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 33.2%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+56} \lor \neg \left(t \leq 6 \cdot 10^{+81}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.1% 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 92.1%

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

   1. associate-+l+ 92.1%

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

   2. associate-*l* 88.2%

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

3. Simplified 88.2%

   \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 27.6%

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

Developer target: 97.4% 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 2024087 
(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)))