Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.8% → 98.4%

Time: 16.0s

Alternatives: 13

Speedup: 0.6×

• 32.4% 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: 92.8% 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: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 1e+305) t_1 (* z (+ y (* a (+ b (/ t z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = z * (y + (a * (b + (t / z))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
    if (t_1 <= 1d+305) then
        tmp = t_1
    else
        tmp = z * (y + (a * (b + (t / z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= 1e+305) {
		tmp = t_1;
	} else {
		tmp = z * (y + (a * (b + (t / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
	tmp = 0
	if t_1 <= 1e+305:
		tmp = t_1
	else:
		tmp = z * (y + (a * (b + (t / z))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y + Float64(a * Float64(b + Float64(t / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= 1e+305)
		tmp = t_1;
	else
		tmp = z * (y + (a * (b + (t / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+305], t$95$1, N[(z * N[(y + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 9.9999999999999994e304

   1. Initial program 100.0%

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

   if 9.9999999999999994e304 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 70.8%

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

   3. Taylor expanded in x around 0 70.8%

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

   4. Taylor expanded in z around inf 92.2%

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

      1. associate-/l* 96.1%

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

      2. distribute-lft-out 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq 10^{+305}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+26} \lor \neg \left(z \leq 1000\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e+26) (not (<= z 1000.0)))
   (* z (+ y (+ (* a (+ b (/ t z))) (/ x z))))
   (+ (+ x (* y z)) (+ (* t a) (* a (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e+26) || !(z <= 1000.0)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = (x + (y * z)) + ((t * a) + (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 <= (-2d+26)) .or. (.not. (z <= 1000.0d0))) then
        tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
    else
        tmp = (x + (y * z)) + ((t * a) + (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 <= -2e+26) || !(z <= 1000.0)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e+26) or not (z <= 1000.0):
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
	else:
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e+26) || !(z <= 1000.0))
		tmp = Float64(z * Float64(y + Float64(Float64(a * Float64(b + Float64(t / z))) + Float64(x / z))));
	else
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(t * a) + 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 <= -2e+26) || ~((z <= 1000.0)))
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	else
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e+26], N[Not[LessEqual[z, 1000.0]], $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[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e26 or 1e3 < z

   1. Initial program 88.8%

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

      1. associate-+l+ 88.8%

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

      2. associate-*l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around inf 98.1%

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

      1. +-commutative 98.1%

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

      2. associate-+l+ 98.1%

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

      3. +-commutative 98.1%

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

      4. associate-/l* 99.9%

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

      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 -2.0000000000000001e26 < z < 1e3

   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* 98.5%

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

   3. Simplified 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+26} \lor \neg \left(z \leq 1000\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-40} \lor \neg \left(z \leq 2.3 \cdot 10^{-78}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e-40) (not (<= z 2.3e-78)))
   (* z (+ y (+ (* a (+ b (/ t z))) (/ x z))))
   (+ x (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e-40) || !(z <= 2.3e-78)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.15d-40)) .or. (.not. (z <= 2.3d-78))) then
        tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
    else
        tmp = x + ((t * a) + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e-40) || !(z <= 2.3e-78)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.15e-40) or not (z <= 2.3e-78):
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
	else:
		tmp = x + ((t * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e-40) || !(z <= 2.3e-78))
		tmp = Float64(z * Float64(y + Float64(Float64(a * Float64(b + Float64(t / z))) + Float64(x / z))));
	else
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.15e-40) || ~((z <= 2.3e-78)))
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	else
		tmp = x + ((t * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e-40], N[Not[LessEqual[z, 2.3e-78]], $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[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e-40 or 2.3000000000000002e-78 < z

   1. Initial program 90.6%

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

      1. associate-+l+ 90.6%

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

      2. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around inf 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-+l+ 97.1%

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

      3. +-commutative 97.1%

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

      4. associate-/l* 98.5%

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

      5. distribute-lft-out 98.5%

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

   7. Simplified 98.5%

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

   if -1.15e-40 < z < 2.3000000000000002e-78

   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* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in b around 0 91.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-40} \lor \neg \left(z \leq 2.3 \cdot 10^{-78}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+203}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+54} \lor \neg \left(y \leq 1.62 \cdot 10^{+69}\right):\\ \;\;\;\;t \cdot a + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6e+203)
   (* z (+ y (* a b)))
   (if (or (<= y -4.1e+54) (not (<= y 1.62e+69)))
     (+ (* t a) (* y z))
     (+ x (* a (+ t (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6e+203) {
		tmp = z * (y + (a * b));
	} else if ((y <= -4.1e+54) || !(y <= 1.62e+69)) {
		tmp = (t * a) + (y * 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 (y <= (-6d+203)) then
        tmp = z * (y + (a * b))
    else if ((y <= (-4.1d+54)) .or. (.not. (y <= 1.62d+69))) then
        tmp = (t * a) + (y * 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 (y <= -6e+203) {
		tmp = z * (y + (a * b));
	} else if ((y <= -4.1e+54) || !(y <= 1.62e+69)) {
		tmp = (t * a) + (y * z);
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6e+203:
		tmp = z * (y + (a * b))
	elif (y <= -4.1e+54) or not (y <= 1.62e+69):
		tmp = (t * a) + (y * z)
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6e+203)
		tmp = Float64(z * Float64(y + Float64(a * b)));
	elseif ((y <= -4.1e+54) || !(y <= 1.62e+69))
		tmp = Float64(Float64(t * a) + Float64(y * 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 (y <= -6e+203)
		tmp = z * (y + (a * b));
	elseif ((y <= -4.1e+54) || ~((y <= 1.62e+69)))
		tmp = (t * a) + (y * z);
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6e+203], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.1e+54], N[Not[LessEqual[y, 1.62e+69]], $MachinePrecision]], N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9999999999999999e203

   1. Initial program 90.0%

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

      1. associate-+l+ 90.0%

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

      2. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in z around inf 90.4%

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

   if -5.9999999999999999e203 < y < -4.09999999999999967e54 or 1.62e69 < y

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0 79.2%

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

   4. Taylor expanded in b around 0 78.0%

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

   if -4.09999999999999967e54 < y < 1.62e69

   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. +-commutative 96.1%

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

      3. fma-define 96.1%

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

      4. associate-*l* 94.9%

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

      5. *-commutative 94.9%

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

      6. *-commutative 94.9%

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

      7. distribute-rgt-out 96.2%

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

      8. remove-double-neg 96.2%

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

      9. *-commutative 96.2%

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

      10. distribute-lft-neg-out 96.2%

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

      11. sub-neg 96.2%

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

      12. sub-neg 96.2%

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

      13. distribute-lft-neg-out 96.2%

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

      14. *-commutative 96.2%

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

      15. remove-double-neg 96.2%

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

      16. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 91.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+203}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+54} \lor \neg \left(y \leq 1.62 \cdot 10^{+69}\right):\\ \;\;\;\;t \cdot a + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+54} \lor \neg \left(y \leq 14\right):\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3e+54) (not (<= y 14.0)))
   (+ x (+ (* t a) (* y z)))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e+54) || !(y <= 14.0)) {
		tmp = x + ((t * a) + (y * 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 ((y <= (-3d+54)) .or. (.not. (y <= 14.0d0))) then
        tmp = x + ((t * a) + (y * 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 ((y <= -3e+54) || !(y <= 14.0)) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3e+54) or not (y <= 14.0):
		tmp = x + ((t * a) + (y * z))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3e+54) || !(y <= 14.0))
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * 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 ((y <= -3e+54) || ~((y <= 14.0)))
		tmp = x + ((t * a) + (y * z));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3e+54], N[Not[LessEqual[y, 14.0]], $MachinePrecision]], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $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 y < -2.9999999999999999e54 or 14 < y

   1. Initial program 90.4%

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

      1. associate-+l+ 90.4%

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

      2. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in b around 0 88.9%

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

   if -2.9999999999999999e54 < y < 14

   1. Initial program 97.2%

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

      1. associate-+l+ 97.2%

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

      2. +-commutative 97.2%

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

      3. fma-define 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* 95.2%

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

      5. *-commutative 95.2%

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

      6. *-commutative 95.2%

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

      7. distribute-rgt-out 96.0%

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

      8. remove-double-neg 96.0%

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

      9. *-commutative 96.0%

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

      10. distribute-lft-neg-out 96.0%

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

      11. sub-neg 96.0%

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

      12. sub-neg 96.0%

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

      13. distribute-lft-neg-out 96.0%

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

      14. *-commutative 96.0%

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

      15. remove-double-neg 96.0%

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

      16. *-commutative 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around 0 91.7%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+54} \lor \neg \left(y \leq 14\right):\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-51} \lor \neg \left(z \leq 2.6 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.5e-51) (not (<= z 2.6e-24)))
   (* z (+ y (* a b)))
   (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.5e-51) || !(z <= 2.6e-24)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.5d-51)) .or. (.not. (z <= 2.6d-24))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.5e-51) || !(z <= 2.6e-24)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.5e-51) or not (z <= 2.6e-24):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.5e-51) || !(z <= 2.6e-24))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.5e-51) || ~((z <= 2.6e-24)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.5e-51], N[Not[LessEqual[z, 2.6e-24]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000002e-51 or 2.6e-24 < z

   1. Initial program 90.4%

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

      1. associate-+l+ 90.4%

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

      2. associate-*l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in z around inf 77.0%

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

   if -2.50000000000000002e-51 < z < 2.6e-24

   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* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around 0 77.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-51} \lor \neg \left(z \leq 2.6 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-34} \lor \neg \left(a \leq 6.4 \cdot 10^{-46}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.15e-34) (not (<= a 6.4e-46)))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.15e-34) || !(a <= 6.4e-46)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.15d-34)) .or. (.not. (a <= 6.4d-46))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.15e-34) || !(a <= 6.4e-46)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.15e-34) or not (a <= 6.4e-46):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.15e-34) || !(a <= 6.4e-46))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.15e-34) || ~((a <= 6.4e-46)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.15e-34], N[Not[LessEqual[a, 6.4e-46]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.15e-34 or 6.3999999999999998e-46 < a

   1. Initial program 90.5%

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

      1. associate-+l+ 90.5%

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

      2. +-commutative 90.5%

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

      3. fma-define 90.5%

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

      4. associate-*l* 93.6%

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

      5. *-commutative 93.6%

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

      6. *-commutative 93.6%

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

      7. distribute-rgt-out 95.5%

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

      8. remove-double-neg 95.5%

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

      9. *-commutative 95.5%

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

      10. distribute-lft-neg-out 95.5%

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

      11. sub-neg 95.5%

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

      12. sub-neg 95.5%

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

      13. distribute-lft-neg-out 95.5%

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

      14. *-commutative 95.5%

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

      15. remove-double-neg 95.5%

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

      16. *-commutative 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 87.9%

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

   6. Taylor expanded in x around 0 76.7%

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

   if -2.15e-34 < a < 6.3999999999999998e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.5%

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

      1. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in x around 0 98.0%

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

      1. associate-*r/ 87.3%

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

   8. Simplified 87.3%

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

   9. Taylor expanded in a around 0 76.7%

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

       1. *-commutative 76.7%

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

   11. Simplified 76.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-34} \lor \neg \left(a \leq 6.4 \cdot 10^{-46}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -500000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -500000000.0)
   (+ x (* y z))
   (if (<= z 1.5e+45) (+ x (* t a)) (* a (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -500000000.0) {
		tmp = x + (y * z);
	} else if (z <= 1.5e+45) {
		tmp = x + (t * a);
	} else {
		tmp = 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 <= (-500000000.0d0)) then
        tmp = x + (y * z)
    else if (z <= 1.5d+45) then
        tmp = x + (t * a)
    else
        tmp = 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 <= -500000000.0) {
		tmp = x + (y * z);
	} else if (z <= 1.5e+45) {
		tmp = x + (t * a);
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -500000000.0:
		tmp = x + (y * z)
	elif z <= 1.5e+45:
		tmp = x + (t * a)
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -500000000.0)
		tmp = Float64(x + Float64(y * z));
	elseif (z <= 1.5e+45)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = 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 <= -500000000.0)
		tmp = x + (y * z);
	elseif (z <= 1.5e+45)
		tmp = x + (t * a);
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -500000000.0], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+45], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e8

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf 83.8%

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

      1. associate-/l* 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in x around 0 89.5%

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

      1. associate-*r/ 88.1%

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

   8. Simplified 88.1%

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

   9. Taylor expanded in a around 0 59.6%

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

       1. *-commutative 59.6%

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

   11. Simplified 59.6%

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

   if -5e8 < z < 1.50000000000000005e45

   1. Initial program 98.6%

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

      1. associate-+l+ 98.6%

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

      2. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 72.3%

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

   if 1.50000000000000005e45 < z

   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. +-commutative 81.9%

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

      3. fma-define 81.9%

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

      4. associate-*l* 86.5%

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

      5. *-commutative 86.5%

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

      6. *-commutative 86.5%

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

      7. distribute-rgt-out 86.5%

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

      8. remove-double-neg 86.5%

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

      9. *-commutative 86.5%

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

      10. distribute-lft-neg-out 86.5%

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

      11. sub-neg 86.5%

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

      12. sub-neg 86.5%

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

      13. distribute-lft-neg-out 86.5%

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

      14. *-commutative 86.5%

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

      15. remove-double-neg 86.5%

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

      16. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around 0 84.5%

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

   6. Taylor expanded in z around inf 62.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -500000000:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+45}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+69}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+44}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5e+69) (* y z) (if (<= z 1.95e+44) (+ x (* t a)) (* a (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5e+69) {
		tmp = y * z;
	} else if (z <= 1.95e+44) {
		tmp = x + (t * a);
	} else {
		tmp = 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+69)) then
        tmp = y * z
    else if (z <= 1.95d+44) then
        tmp = x + (t * a)
    else
        tmp = 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+69) {
		tmp = y * z;
	} else if (z <= 1.95e+44) {
		tmp = x + (t * a);
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5e+69:
		tmp = y * z
	elif z <= 1.95e+44:
		tmp = x + (t * a)
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5e+69)
		tmp = Float64(y * z);
	elseif (z <= 1.95e+44)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = 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+69)
		tmp = y * z;
	elseif (z <= 1.95e+44)
		tmp = x + (t * a);
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5e+69], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.95e+44], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000036e69

   1. Initial program 89.8%

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

      1. associate-+l+ 89.8%

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

      2. associate-*l* 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 inf 74.0%

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

      1. associate-/l* 69.8%

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

      2. associate-/l* 75.7%

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

      3. *-commutative 75.7%

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

   7. Simplified 75.7%

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

   8. Taylor expanded in y around inf 55.4%

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

      1. *-commutative 55.4%

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

   10. Simplified 55.4%

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

   if -5.00000000000000036e69 < z < 1.9500000000000001e44

   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* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around 0 68.8%

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

   if 1.9500000000000001e44 < z

   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. +-commutative 81.9%

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

      3. fma-define 81.9%

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

      4. associate-*l* 86.5%

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

      5. *-commutative 86.5%

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

      6. *-commutative 86.5%

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

      7. distribute-rgt-out 86.5%

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

      8. remove-double-neg 86.5%

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

      9. *-commutative 86.5%

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

      10. distribute-lft-neg-out 86.5%

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

      11. sub-neg 86.5%

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

      12. sub-neg 86.5%

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

      13. distribute-lft-neg-out 86.5%

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

      14. *-commutative 86.5%

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

      15. remove-double-neg 86.5%

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

      16. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around 0 84.5%

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

   6. Taylor expanded in z around inf 62.3%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+69}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+44}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15.2:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+45}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -15.2) (* y z) (if (<= z 2.15e+45) (* t a) (* a (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -15.2) {
		tmp = y * z;
	} else if (z <= 2.15e+45) {
		tmp = t * a;
	} else {
		tmp = 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 <= (-15.2d0)) then
        tmp = y * z
    else if (z <= 2.15d+45) then
        tmp = t * a
    else
        tmp = 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 <= -15.2) {
		tmp = y * z;
	} else if (z <= 2.15e+45) {
		tmp = t * a;
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -15.2:
		tmp = y * z
	elif z <= 2.15e+45:
		tmp = t * a
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -15.2)
		tmp = Float64(y * z);
	elseif (z <= 2.15e+45)
		tmp = Float64(t * a);
	else
		tmp = 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 <= -15.2)
		tmp = y * z;
	elseif (z <= 2.15e+45)
		tmp = t * a;
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -15.2], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.15e+45], N[(t * a), $MachinePrecision], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -15.199999999999999

   1. Initial program 92.6%

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

      1. associate-+l+ 92.6%

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

      2. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in t around inf 74.4%

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

      1. associate-/l* 71.4%

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

      2. associate-/l* 74.1%

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

      3. *-commutative 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in y around inf 49.8%

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

      1. *-commutative 49.8%

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

   10. Simplified 49.8%

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

   if -15.199999999999999 < z < 2.1500000000000002e45

   1. Initial program 98.6%

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

      1. associate-+l+ 98.6%

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

      2. associate-*l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 72.1%

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

   6. Taylor expanded in x around 0 47.1%

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

   if 2.1500000000000002e45 < z

   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. +-commutative 81.9%

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

      3. fma-define 81.9%

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

      4. associate-*l* 86.5%

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

      5. *-commutative 86.5%

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

      6. *-commutative 86.5%

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

      7. distribute-rgt-out 86.5%

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

      8. remove-double-neg 86.5%

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

      9. *-commutative 86.5%

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

      10. distribute-lft-neg-out 86.5%

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

      11. sub-neg 86.5%

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

      12. sub-neg 86.5%

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

      13. distribute-lft-neg-out 86.5%

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

      14. *-commutative 86.5%

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

      15. remove-double-neg 86.5%

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

      16. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in y around 0 84.5%

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

   6. Taylor expanded in z around inf 62.3%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15.2:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+45}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+28} \lor \neg \left(y \leq 5.5 \cdot 10^{+62}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.3e+28) (not (<= y 5.5e+62))) (* y z) (* t a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+28) || !(y <= 5.5e+62)) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.3d+28)) .or. (.not. (y <= 5.5d+62))) then
        tmp = y * z
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+28) || !(y <= 5.5e+62)) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.3e+28) or not (y <= 5.5e+62):
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.3e+28) || !(y <= 5.5e+62))
		tmp = Float64(y * z);
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.3e+28) || ~((y <= 5.5e+62)))
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.3e+28], N[Not[LessEqual[y, 5.5e+62]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e28 or 5.4999999999999997e62 < y

   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* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in t around inf 77.0%

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

      1. associate-/l* 76.1%

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

      2. associate-/l* 76.9%

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

      3. *-commutative 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in y around inf 56.1%

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

      1. *-commutative 56.1%

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

   10. Simplified 56.1%

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

   if -3.3e28 < y < 5.4999999999999997e62

   1. Initial program 95.8%

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

      1. associate-+l+ 95.8%

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

      2. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in z around 0 64.0%

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

   6. Taylor expanded in x around 0 40.0%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+28} \lor \neg \left(y \leq 5.5 \cdot 10^{+62}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{+62}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.8e+60) x (if (<= x 3.75e+62) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+60) {
		tmp = x;
	} else if (x <= 3.75e+62) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.8d+60)) then
        tmp = x
    else if (x <= 3.75d+62) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+60) {
		tmp = x;
	} else if (x <= 3.75e+62) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.8e+60:
		tmp = x
	elif x <= 3.75e+62:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.8e+60)
		tmp = x;
	elseif (x <= 3.75e+62)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.8e+60)
		tmp = x;
	elseif (x <= 3.75e+62)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.8e+60], x, If[LessEqual[x, 3.75e+62], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.79999999999999984e60 or 3.74999999999999999e62 < x

   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* 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 z around 0 60.7%

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

   6. Taylor expanded in x around inf 44.9%

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

   if -8.79999999999999984e60 < x < 3.74999999999999999e62

   1. Initial program 93.3%

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

      1. associate-+l+ 93.3%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around 0 46.7%

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

   6. Taylor expanded in x around 0 40.2%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{+62}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 25.5% 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 94.2%

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

   1. associate-+l+ 94.2%

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

   2. associate-*l* 93.1%

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

3. Simplified 93.1%

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

5. Taylor expanded in z around 0 51.7%

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

6. Taylor expanded in x around inf 21.3%

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

Developer Target 1: 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 2024180 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

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