Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.4% → 99.5%

Time: 10.2s

Alternatives: 15

Speedup: 0.7×

• 31.9% 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: 92.4% 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: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+25} \lor \neg \left(z \leq 4 \cdot 10^{-21}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot \left(z \cdot b\right) + a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+25) (not (<= z 4e-21)))
   (* z (+ y (+ (* a (+ b (/ t z))) (/ x z))))
   (+ (+ x (* z y)) (+ (* a (* z b)) (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+25) || !(z <= 4e-21)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = (x + (z * y)) + ((a * (z * b)) + (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 <= (-1.4d+25)) .or. (.not. (z <= 4d-21))) then
        tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
    else
        tmp = (x + (z * y)) + ((a * (z * b)) + (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 <= -1.4e+25) || !(z <= 4e-21)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = (x + (z * y)) + ((a * (z * b)) + (a * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e+25) or not (z <= 4e-21):
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
	else:
		tmp = (x + (z * y)) + ((a * (z * b)) + (a * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+25) || !(z <= 4e-21))
		tmp = Float64(z * Float64(y + Float64(Float64(a * Float64(b + Float64(t / z))) + Float64(x / z))));
	else
		tmp = Float64(Float64(x + Float64(z * y)) + Float64(Float64(a * Float64(z * b)) + Float64(a * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.4e+25) || ~((z <= 4e-21)))
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	else
		tmp = (x + (z * y)) + ((a * (z * b)) + (a * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+25], N[Not[LessEqual[z, 4e-21]], $MachinePrecision]], N[(z * N[(y + N[(N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4000000000000001e25 or 3.99999999999999963e-21 < z

   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* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in z around inf 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-+r+ 96.6%

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

      3. associate-/l* 99.1%

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

      4. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   if -1.4000000000000001e25 < z < 3.99999999999999963e-21

   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
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+25} \lor \neg \left(z \leq 4 \cdot 10^{-21}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot \left(z \cdot b\right) + a \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-54} \lor \neg \left(z \leq 1.95 \cdot 10^{-87}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(z \cdot b\right) + a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.35e-54) (not (<= z 1.95e-87)))
   (* z (+ y (+ (* a (+ b (/ t z))) (/ x z))))
   (+ x (+ (* a (* z b)) (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.35e-54) || !(z <= 1.95e-87)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = x + ((a * (z * b)) + (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 <= (-1.35d-54)) .or. (.not. (z <= 1.95d-87))) then
        tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
    else
        tmp = x + ((a * (z * b)) + (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 <= -1.35e-54) || !(z <= 1.95e-87)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = x + ((a * (z * b)) + (a * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.35e-54) or not (z <= 1.95e-87):
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
	else:
		tmp = x + ((a * (z * b)) + (a * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.35e-54) || !(z <= 1.95e-87))
		tmp = Float64(z * Float64(y + Float64(Float64(a * Float64(b + Float64(t / z))) + Float64(x / z))));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(z * b)) + Float64(a * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.35e-54) || ~((z <= 1.95e-87)))
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	else
		tmp = x + ((a * (z * b)) + (a * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.35e-54], N[Not[LessEqual[z, 1.95e-87]], $MachinePrecision]], N[(z * N[(y + N[(N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000013e-54 or 1.9499999999999999e-87 < z

   1. Initial program 92.9%

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

      1. associate-+l+ 92.9%

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

      2. associate-*l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in z around inf 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-+r+ 95.5%

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

      3. associate-/l* 97.4%

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

      4. distribute-lft-out 98.7%

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

   7. Simplified 98.7%

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

   if -1.35000000000000013e-54 < z < 1.9499999999999999e-87

   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 y around 0 93.2%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-54} \lor \neg \left(z \leq 1.95 \cdot 10^{-87}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(z \cdot b\right) + a \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+67}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (+ y (* a b)))))
   (if (<= z -1.2e+124)
     t_1
     (if (<= z -1.6e-69) (+ x (* z y)) (if (<= z 8e+67) (+ x (* a t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -1.2e+124) {
		tmp = t_1;
	} else if (z <= -1.6e-69) {
		tmp = x + (z * y);
	} else if (z <= 8e+67) {
		tmp = x + (a * t);
	} 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 * (y + (a * b))
    if (z <= (-1.2d+124)) then
        tmp = t_1
    else if (z <= (-1.6d-69)) then
        tmp = x + (z * y)
    else if (z <= 8d+67) then
        tmp = x + (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y + (a * b));
	double tmp;
	if (z <= -1.2e+124) {
		tmp = t_1;
	} else if (z <= -1.6e-69) {
		tmp = x + (z * y);
	} else if (z <= 8e+67) {
		tmp = x + (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y + (a * b))
	tmp = 0
	if z <= -1.2e+124:
		tmp = t_1
	elif z <= -1.6e-69:
		tmp = x + (z * y)
	elif z <= 8e+67:
		tmp = x + (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -1.2e+124)
		tmp = t_1;
	elseif (z <= -1.6e-69)
		tmp = Float64(x + Float64(z * y));
	elseif (z <= 8e+67)
		tmp = Float64(x + Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -1.2e+124)
		tmp = t_1;
	elseif (z <= -1.6e-69)
		tmp = x + (z * y);
	elseif (z <= 8e+67)
		tmp = x + (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+124], t$95$1, If[LessEqual[z, -1.6e-69], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+67], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000003e124 or 7.99999999999999986e67 < z

   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* 79.0%

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

   3. Simplified 79.0%

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

   5. Taylor expanded in z around inf 90.1%

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

      1. +-commutative 90.1%

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

   7. Simplified 90.1%

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

   if -1.20000000000000003e124 < z < -1.59999999999999999e-69

   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* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around 0 67.9%

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

   if -1.59999999999999999e-69 < z < 7.99999999999999986e67

   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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 80.5%

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

      1. +-commutative 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+67}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-71} \lor \neg \left(z \leq 8 \cdot 10^{+67}\right):\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7e+130)
   (* b (* z a))
   (if (or (<= z -2.4e-71) (not (<= z 8e+67))) (+ x (* z y)) (+ x (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7e+130) {
		tmp = b * (z * a);
	} else if ((z <= -2.4e-71) || !(z <= 8e+67)) {
		tmp = x + (z * y);
	} 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 <= (-7d+130)) then
        tmp = b * (z * a)
    else if ((z <= (-2.4d-71)) .or. (.not. (z <= 8d+67))) then
        tmp = x + (z * y)
    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 <= -7e+130) {
		tmp = b * (z * a);
	} else if ((z <= -2.4e-71) || !(z <= 8e+67)) {
		tmp = x + (z * y);
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7e+130:
		tmp = b * (z * a)
	elif (z <= -2.4e-71) or not (z <= 8e+67):
		tmp = x + (z * y)
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7e+130)
		tmp = Float64(b * Float64(z * a));
	elseif ((z <= -2.4e-71) || !(z <= 8e+67))
		tmp = Float64(x + Float64(z * y));
	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 <= -7e+130)
		tmp = b * (z * a);
	elseif ((z <= -2.4e-71) || ~((z <= 8e+67)))
		tmp = x + (z * y);
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7e+130], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.4e-71], N[Not[LessEqual[z, 8e+67]], $MachinePrecision]], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000002e130

   1. Initial program 83.6%

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

      1. associate-+l+ 83.6%

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

      2. associate-*l* 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in a around inf 79.3%

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

   6. Taylor expanded in b around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-*l* 60.8%

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

   8. Simplified 60.8%

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

   if -7.0000000000000002e130 < z < -2.4e-71 or 7.99999999999999986e67 < z

   1. Initial program 94.5%

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

      1. associate-+l+ 94.5%

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

      2. associate-*l* 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in a around 0 67.5%

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

   if -2.4e-71 < z < 7.99999999999999986e67

   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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 80.5%

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

      1. +-commutative 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-71} \lor \neg \left(z \leq 8 \cdot 10^{+67}\right):\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+34} \lor \neg \left(a \leq 6.5 \cdot 10^{+141}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1e+105)
   (* a (* z b))
   (if (or (<= a -8.5e+34) (not (<= a 6.5e+141))) (* a t) (+ x (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1e+105) {
		tmp = a * (z * b);
	} else if ((a <= -8.5e+34) || !(a <= 6.5e+141)) {
		tmp = a * t;
	} 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 <= (-1d+105)) then
        tmp = a * (z * b)
    else if ((a <= (-8.5d+34)) .or. (.not. (a <= 6.5d+141))) then
        tmp = a * t
    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 <= -1e+105) {
		tmp = a * (z * b);
	} else if ((a <= -8.5e+34) || !(a <= 6.5e+141)) {
		tmp = a * t;
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1e+105:
		tmp = a * (z * b)
	elif (a <= -8.5e+34) or not (a <= 6.5e+141):
		tmp = a * t
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1e+105)
		tmp = Float64(a * Float64(z * b));
	elseif ((a <= -8.5e+34) || !(a <= 6.5e+141))
		tmp = Float64(a * t);
	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 <= -1e+105)
		tmp = a * (z * b);
	elseif ((a <= -8.5e+34) || ~((a <= 6.5e+141)))
		tmp = a * t;
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1e+105], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -8.5e+34], N[Not[LessEqual[a, 6.5e+141]], $MachinePrecision]], N[(a * t), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.9999999999999994e104

   1. Initial program 84.5%

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

      1. associate-+l+ 84.5%

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

      2. associate-*l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. associate-+r+ 74.2%

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

      3. associate-/l* 76.8%

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

      4. distribute-lft-out 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in b around inf 51.5%

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

      1. *-commutative 51.5%

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

   10. Simplified 51.5%

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

   if -9.9999999999999994e104 < a < -8.5000000000000003e34 or 6.50000000000000053e141 < a

   1. Initial program 94.6%

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

      1. associate-+l+ 94.6%

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

      2. associate-*l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. associate-+r+ 70.7%

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

      3. associate-/l* 72.4%

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

      4. distribute-lft-out 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in t around inf 54.8%

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

   if -8.5000000000000003e34 < a < 6.50000000000000053e141

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in a around 0 64.3%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+34} \lor \neg \left(a \leq 6.5 \cdot 10^{+141}\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot a\right) + \left(\left(x + z \cdot y\right) + a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.5e+85)
   (* z (+ y (+ (* a (+ b (/ t z))) (/ x z))))
   (+ (* b (* z a)) (+ (+ x (* z y)) (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+85) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = (b * (z * a)) + ((x + (z * y)) + (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 <= (-8.5d+85)) then
        tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
    else
        tmp = (b * (z * a)) + ((x + (z * y)) + (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 <= -8.5e+85) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = (b * (z * a)) + ((x + (z * y)) + (a * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.5e+85:
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
	else:
		tmp = (b * (z * a)) + ((x + (z * y)) + (a * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.5e+85)
		tmp = Float64(z * Float64(y + Float64(Float64(a * Float64(b + Float64(t / z))) + Float64(x / z))));
	else
		tmp = Float64(Float64(b * Float64(z * a)) + Float64(Float64(x + Float64(z * y)) + Float64(a * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.5e+85)
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	else
		tmp = (b * (z * a)) + ((x + (z * y)) + (a * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.5e+85], N[(z * N[(y + N[(N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision] + N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999994e85

   1. Initial program 80.2%

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

      1. associate-+l+ 80.2%

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

      2. associate-*l* 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in z around inf 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-+r+ 93.2%

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

      3. associate-/l* 97.7%

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

      4. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   if -8.4999999999999994e85 < z

   1. Initial program 99.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot a\right) + \left(\left(x + z \cdot y\right) + a \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-58} \lor \neg \left(z \leq 7.5 \cdot 10^{+67}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e-58) (not (<= z 7.5e+67)))
   (+ x (* z (+ y (* a b))))
   (+ (+ x (* z y)) (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e-58) || !(z <= 7.5e+67)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (z * y)) + (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 <= (-2.3d-58)) .or. (.not. (z <= 7.5d+67))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = (x + (z * y)) + (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 <= -2.3e-58) || !(z <= 7.5e+67)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (z * y)) + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e-58) or not (z <= 7.5e+67):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = (x + (z * y)) + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e-58) || !(z <= 7.5e+67))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(x + Float64(z * y)) + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.3e-58) || ~((z <= 7.5e+67)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = (x + (z * y)) + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e-58], N[Not[LessEqual[z, 7.5e+67]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999999e-58 or 7.5000000000000005e67 < z

   1. Initial program 91.2%

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

      1. associate-+l+ 91.2%

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

      2. associate-*l* 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in t around 0 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-*r* 90.5%

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

      3. distribute-rgt-in 92.9%

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

   7. Simplified 92.9%

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

   if -2.2999999999999999e-58 < z < 7.5000000000000005e67

   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* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in t around inf 90.5%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-58} \lor \neg \left(z \leq 7.5 \cdot 10^{+67}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-69} \lor \neg \left(z \leq 2.2 \cdot 10^{+70}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.7e-69) (not (<= z 2.2e+70)))
   (+ x (* 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 <= -1.7e-69) || !(z <= 2.2e+70)) {
		tmp = x + (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 <= (-1.7d-69)) .or. (.not. (z <= 2.2d+70))) then
        tmp = x + (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 <= -1.7e-69) || !(z <= 2.2e+70)) {
		tmp = x + (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 <= -1.7e-69) or not (z <= 2.2e+70):
		tmp = x + (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 <= -1.7e-69) || !(z <= 2.2e+70))
		tmp = Float64(x + 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 <= -1.7e-69) || ~((z <= 2.2e+70)))
		tmp = x + (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, -1.7e-69], N[Not[LessEqual[z, 2.2e+70]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $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 < -1.70000000000000004e-69 or 2.20000000000000001e70 < z

   1. Initial program 91.4%

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

      1. associate-+l+ 91.4%

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

      2. associate-*l* 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in t around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-*r* 90.7%

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

      3. distribute-rgt-in 93.1%

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

   7. Simplified 93.1%

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

   if -1.70000000000000004e-69 < z < 2.20000000000000001e70

   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. +-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-*l* 99.2%

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

      5. *-commutative 99.2%

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

      6. *-commutative 99.2%

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

      7. distribute-rgt-out 99.2%

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

      8. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 89.4%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-69} \lor \neg \left(z \leq 2.2 \cdot 10^{+70}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+121} \lor \neg \left(z \leq 1.02 \cdot 10^{+68}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e+121) (not (<= z 1.02e+68)))
   (* 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 <= -3.5e+121) || !(z <= 1.02e+68)) {
		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 <= (-3.5d+121)) .or. (.not. (z <= 1.02d+68))) 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 <= -3.5e+121) || !(z <= 1.02e+68)) {
		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 <= -3.5e+121) or not (z <= 1.02e+68):
		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 <= -3.5e+121) || !(z <= 1.02e+68))
		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 <= -3.5e+121) || ~((z <= 1.02e+68)))
		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, -3.5e+121], N[Not[LessEqual[z, 1.02e+68]], $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 < -3.5e121 or 1.02e68 < z

   1. Initial program 91.3%

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

      1. associate-+l+ 91.3%

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

      2. associate-*l* 79.7%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in z around inf 89.4%

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

      1. +-commutative 89.4%

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

   7. Simplified 89.4%

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

   if -3.5e121 < z < 1.02e68

   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. +-commutative 98.2%

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

      3. fma-define 98.2%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. *-commutative 98.2%

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

      7. distribute-rgt-out 99.4%

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

      8. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around 0 86.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+121} \lor \neg \left(z \leq 1.02 \cdot 10^{+68}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+68}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.1e+124)
   (* b (* z a))
   (if (<= z -3.2e-83) x (if (<= z 6.5e+68) (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.1e+124) {
		tmp = b * (z * a);
	} else if (z <= -3.2e-83) {
		tmp = x;
	} else if (z <= 6.5e+68) {
		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 <= (-1.1d+124)) then
        tmp = b * (z * a)
    else if (z <= (-3.2d-83)) then
        tmp = x
    else if (z <= 6.5d+68) 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 <= -1.1e+124) {
		tmp = b * (z * a);
	} else if (z <= -3.2e-83) {
		tmp = x;
	} else if (z <= 6.5e+68) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.1e+124:
		tmp = b * (z * a)
	elif z <= -3.2e-83:
		tmp = x
	elif z <= 6.5e+68:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.1e+124)
		tmp = Float64(b * Float64(z * a));
	elseif (z <= -3.2e-83)
		tmp = x;
	elseif (z <= 6.5e+68)
		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 <= -1.1e+124)
		tmp = b * (z * a);
	elseif (z <= -3.2e-83)
		tmp = x;
	elseif (z <= 6.5e+68)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.1e+124], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e-83], x, If[LessEqual[z, 6.5e+68], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e124

   1. Initial program 83.6%

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

      1. associate-+l+ 83.6%

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

      2. associate-*l* 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in a around inf 79.3%

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

   6. Taylor expanded in b around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-*l* 60.8%

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

   8. Simplified 60.8%

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

   if -1.1e124 < z < -3.2000000000000001e-83

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in x around inf 43.1%

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

   if -3.2000000000000001e-83 < z < 6.5000000000000005e68

   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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. associate-+r+ 64.8%

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

      3. associate-/l* 58.5%

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

      4. distribute-lft-out 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around inf 51.2%

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

   if 6.5000000000000005e68 < z

   1. Initial program 96.1%

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

      1. associate-+l+ 96.1%

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

      2. associate-*l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

   7. Simplified 61.2%

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

Alternative 11: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+67}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.2e+124)
   (* a (* z b))
   (if (<= z -1.95e-84) x (if (<= z 6.5e+67) (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e+124) {
		tmp = a * (z * b);
	} else if (z <= -1.95e-84) {
		tmp = x;
	} else if (z <= 6.5e+67) {
		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 <= (-4.2d+124)) then
        tmp = a * (z * b)
    else if (z <= (-1.95d-84)) then
        tmp = x
    else if (z <= 6.5d+67) 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 <= -4.2e+124) {
		tmp = a * (z * b);
	} else if (z <= -1.95e-84) {
		tmp = x;
	} else if (z <= 6.5e+67) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.2e+124:
		tmp = a * (z * b)
	elif z <= -1.95e-84:
		tmp = x
	elif z <= 6.5e+67:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.2e+124)
		tmp = Float64(a * Float64(z * b));
	elseif (z <= -1.95e-84)
		tmp = x;
	elseif (z <= 6.5e+67)
		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 <= -4.2e+124)
		tmp = a * (z * b);
	elseif (z <= -1.95e-84)
		tmp = x;
	elseif (z <= 6.5e+67)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.2e+124], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-84], x, If[LessEqual[z, 6.5e+67], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.20000000000000023e124

   1. Initial program 83.6%

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

      1. associate-+l+ 83.6%

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

      2. associate-*l* 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in z around inf 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-+r+ 94.3%

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

      3. associate-/l* 97.1%

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

      4. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in b around inf 55.8%

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

      1. *-commutative 55.8%

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

   10. Simplified 55.8%

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

   if -4.20000000000000023e124 < z < -1.95000000000000011e-84

   1. Initial program 93.0%

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

      1. associate-+l+ 93.0%

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

      2. associate-*l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in x around inf 43.1%

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

   if -1.95000000000000011e-84 < z < 6.4999999999999995e67

   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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. associate-+r+ 64.8%

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

      3. associate-/l* 58.5%

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

      4. distribute-lft-out 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around inf 51.2%

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

   if 6.4999999999999995e67 < z

   1. Initial program 96.1%

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

      1. associate-+l+ 96.1%

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

      2. associate-*l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

   7. Simplified 61.2%

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

Alternative 12: 38.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+148}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+68}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5e+148)
   (* z y)
   (if (<= z -2.85e-90) x (if (<= z 2.7e+68) (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5e+148) {
		tmp = z * y;
	} else if (z <= -2.85e-90) {
		tmp = x;
	} else if (z <= 2.7e+68) {
		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 <= (-5d+148)) then
        tmp = z * y
    else if (z <= (-2.85d-90)) then
        tmp = x
    else if (z <= 2.7d+68) 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 <= -5e+148) {
		tmp = z * y;
	} else if (z <= -2.85e-90) {
		tmp = x;
	} else if (z <= 2.7e+68) {
		tmp = a * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5e+148:
		tmp = z * y
	elif z <= -2.85e-90:
		tmp = x
	elif z <= 2.7e+68:
		tmp = a * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5e+148)
		tmp = Float64(z * y);
	elseif (z <= -2.85e-90)
		tmp = x;
	elseif (z <= 2.7e+68)
		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 <= -5e+148)
		tmp = z * y;
	elseif (z <= -2.85e-90)
		tmp = x;
	elseif (z <= 2.7e+68)
		tmp = a * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5e+148], N[(z * y), $MachinePrecision], If[LessEqual[z, -2.85e-90], x, If[LessEqual[z, 2.7e+68], N[(a * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000024e148 or 2.69999999999999991e68 < z

   1. Initial program 91.7%

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

      1. associate-+l+ 91.7%

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

      2. associate-*l* 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in y around inf 51.7%

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

      1. *-commutative 51.7%

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

   7. Simplified 51.7%

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

   if -5.00000000000000024e148 < z < -2.8500000000000001e-90

   1. Initial program 91.6%

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

      1. associate-+l+ 91.6%

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

      2. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 41.8%

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

   if -2.8500000000000001e-90 < z < 2.69999999999999991e68

   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* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. associate-+r+ 64.8%

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

      3. associate-/l* 58.5%

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

      4. distribute-lft-out 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around inf 51.2%

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

Alternative 13: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-30} \lor \neg \left(a \leq 6500\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.8e-30) (not (<= a 6500.0)))
   (* a (+ t (* z b)))
   (+ x (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.8e-30) || !(a <= 6500.0)) {
		tmp = a * (t + (z * b));
	} 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 <= (-2.8d-30)) .or. (.not. (a <= 6500.0d0))) then
        tmp = a * (t + (z * b))
    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 <= -2.8e-30) || !(a <= 6500.0)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.8e-30) or not (a <= 6500.0):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.8e-30) || !(a <= 6500.0))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	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 <= -2.8e-30) || ~((a <= 6500.0)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.8e-30], N[Not[LessEqual[a, 6500.0]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.79999999999999988e-30 or 6500 < a

   1. Initial program 91.5%

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

      1. associate-+l+ 91.5%

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

      2. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in a around inf 96.9%

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

   6. Taylor expanded in a around inf 75.6%

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

      1. *-commutative 75.6%

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

   8. Simplified 75.6%

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

   if -2.79999999999999988e-30 < a < 6500

   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* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in a around 0 70.4%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-30} \lor \neg \left(a \leq 6500\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+53}:\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.85e+57) x (if (<= x 2.9e+53) (* a t) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.85e+57) {
		tmp = x;
	} else if (x <= 2.9e+53) {
		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 (x <= (-2.85d+57)) then
        tmp = x
    else if (x <= 2.9d+53) 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 (x <= -2.85e+57) {
		tmp = x;
	} else if (x <= 2.9e+53) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.85e+57:
		tmp = x
	elif x <= 2.9e+53:
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.85e+57)
		tmp = x;
	elseif (x <= 2.9e+53)
		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 (x <= -2.85e+57)
		tmp = x;
	elseif (x <= 2.9e+53)
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.85e+57], x, If[LessEqual[x, 2.9e+53], N[(a * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8499999999999999e57 or 2.9000000000000002e53 < x

   1. Initial program 96.4%

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

      1. associate-+l+ 96.4%

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

      2. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf 46.7%

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

   if -2.8499999999999999e57 < x < 2.9000000000000002e53

   1. Initial program 95.2%

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

      1. associate-+l+ 95.2%

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

      2. associate-*l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in z around inf 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-+r+ 89.3%

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

      3. associate-/l* 83.9%

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

      4. distribute-lft-out 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in t around inf 40.6%

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

Alternative 15: 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 95.7%

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

   1. associate-+l+ 95.7%

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

   2. associate-*l* 91.6%

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

3. Simplified 91.6%

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

5. Taylor expanded in x around inf 24.8%

   \[\leadsto \color{blue}{x} \]
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 2024091 
(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)))