Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.0% → 95.9%

Time: 11.7s

Alternatives: 11

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: 92.0% 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: 95.9% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$1 + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 + N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(a * N[(N[(t / y), $MachinePrecision] + N[(z * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z + N[(x / y), $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)) < +inf.0

   1. Initial program 96.8%

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

      1. associate-+l+ 96.8%

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

      2. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 21.4%

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

   3. Simplified 21.4%

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

   5. Taylor expanded in y around inf 35.7%

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

      1. +-commutative 35.7%

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

      2. +-commutative 35.7%

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

      3. associate-+l+ 35.7%

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

      4. associate-/l* 50.0%

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

      5. associate-/l* 71.4%

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

      6. distribute-lft-out 85.7%

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

      7. *-commutative 85.7%

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

      8. associate-/l* 92.9%

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

      9. +-commutative 92.9%

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

   7. Simplified 92.9%

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

4. Final simplification 97.0%

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

Alternative 2: 95.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= (+ (+ t_1 (* t a)) (* (* z a) b)) INFINITY)
     (+ t_1 (+ (* a (* z b)) (* t a)))
     (+ x (* z (* 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);
	double tmp;
	if (((t_1 + (t * a)) + ((z * a) * b)) <= ((double) INFINITY)) {
		tmp = t_1 + ((a * (z * b)) + (t * a));
	} else {
		tmp = x + (z * (a * (b + (t / z))));
	}
	return tmp;
}

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (Float64(Float64(t_1 + Float64(t * a)) + Float64(Float64(z * a) * b)) <= Inf)
		tmp = Float64(t_1 + Float64(Float64(a * Float64(z * b)) + Float64(t * a)));
	else
		tmp = Float64(x + Float64(z * 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);
	tmp = 0.0;
	if (((t_1 + (t * a)) + ((z * a) * b)) <= Inf)
		tmp = t_1 + ((a * (z * b)) + (t * a));
	else
		tmp = x + (z * (a * (b + (t / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$1 + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 + N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * 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)) < +inf.0

   1. Initial program 96.8%

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

      1. associate-+l+ 96.8%

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

      2. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 21.4%

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

   3. Simplified 21.4%

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

      1. add-cube-cbrt 21.4%

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

      2. pow3 21.4%

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

   6. Applied egg-rr 21.4%

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

   7. Taylor expanded in z around inf 42.9%

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

      1. +-commutative 42.9%

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

      2. associate-/l* 57.1%

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

      3. distribute-lft-out 57.1%

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

   9. Simplified 57.1%

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

   10. Taylor expanded in y around 0 85.7%

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

       1. associate-*r* 85.7%

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

       2. *-commutative 85.7%

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

       3. +-commutative 85.7%

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

       4. associate-*r* 85.7%

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

       5. +-commutative 85.7%

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

   12. Simplified 85.7%

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

4. Final simplification 96.6%

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

Alternative 3: 92.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-127} \lor \neg \left(z \leq 7.5 \cdot 10^{-155}\right):\\ \;\;\;\;\left(x + y \cdot z\right) + z \cdot \left(a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7e-127) (not (<= z 7.5e-155)))
   (+ (+ x (* y z)) (* z (* a (+ b (/ t z)))))
   (+ x (+ (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e-127) || !(z <= 7.5e-155)) {
		tmp = (x + (y * z)) + (z * (a * (b + (t / z))));
	} else {
		tmp = x + ((y * z) + (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7d-127)) .or. (.not. (z <= 7.5d-155))) then
        tmp = (x + (y * z)) + (z * (a * (b + (t / z))))
    else
        tmp = x + ((y * z) + (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e-127) || !(z <= 7.5e-155)) {
		tmp = (x + (y * z)) + (z * (a * (b + (t / z))));
	} else {
		tmp = x + ((y * z) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7e-127) or not (z <= 7.5e-155):
		tmp = (x + (y * z)) + (z * (a * (b + (t / z))))
	else:
		tmp = x + ((y * z) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7e-127) || !(z <= 7.5e-155))
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(z * Float64(a * Float64(b + Float64(t / z)))));
	else
		tmp = Float64(x + Float64(Float64(y * z) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7e-127) || ~((z <= 7.5e-155)))
		tmp = (x + (y * z)) + (z * (a * (b + (t / z))));
	else
		tmp = x + ((y * z) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7e-127], N[Not[LessEqual[z, 7.5e-155]], $MachinePrecision]], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(z * N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999979e-127 or 7.5000000000000006e-155 < z

   1. Initial program 88.1%

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

      1. associate-+l+ 88.1%

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

      2. associate-*l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around inf 95.0%

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

      1. associate-/l* 95.1%

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

      2. distribute-lft-out 95.1%

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

   7. Simplified 95.1%

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

   if -6.99999999999999979e-127 < z < 7.5000000000000006e-155

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 93.4%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-127} \lor \neg \left(z \leq 7.5 \cdot 10^{-155}\right):\\ \;\;\;\;\left(x + y \cdot z\right) + z \cdot \left(a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+230}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-38} \lor \neg \left(z \leq 4.8 \cdot 10^{-67}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8e+230)
   (* z (* a b))
   (if (or (<= z -2.8e-38) (not (<= z 4.8e-67))) (+ x (* y z)) (+ x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8e+230) {
		tmp = z * (a * b);
	} else if ((z <= -2.8e-38) || !(z <= 4.8e-67)) {
		tmp = x + (y * z);
	} 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 <= (-8d+230)) then
        tmp = z * (a * b)
    else if ((z <= (-2.8d-38)) .or. (.not. (z <= 4.8d-67))) then
        tmp = x + (y * z)
    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 <= -8e+230) {
		tmp = z * (a * b);
	} else if ((z <= -2.8e-38) || !(z <= 4.8e-67)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8e+230:
		tmp = z * (a * b)
	elif (z <= -2.8e-38) or not (z <= 4.8e-67):
		tmp = x + (y * z)
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8e+230)
		tmp = Float64(z * Float64(a * b));
	elseif ((z <= -2.8e-38) || !(z <= 4.8e-67))
		tmp = Float64(x + Float64(y * z));
	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 <= -8e+230)
		tmp = z * (a * b);
	elseif ((z <= -2.8e-38) || ~((z <= 4.8e-67)))
		tmp = x + (y * z);
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8e+230], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.8e-38], N[Not[LessEqual[z, 4.8e-67]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000008e230

   1. Initial program 66.5%

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

      1. associate-+l+ 66.5%

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

      2. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in z around inf 92.8%

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

   6. Taylor expanded in y around 0 78.8%

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

      1. *-commutative 78.8%

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

   8. Simplified 78.8%

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

   if -8.0000000000000008e230 < z < -2.8e-38 or 4.8e-67 < z

   1. Initial program 87.2%

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

      1. associate-+l+ 87.2%

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

      2. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in a around 0 55.7%

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

   if -2.8e-38 < z < 4.8e-67

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 81.5%

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

      1. +-commutative 81.5%

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

   7. Simplified 81.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+230}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-38} \lor \neg \left(z \leq 4.8 \cdot 10^{-67}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-28} \lor \neg \left(z \leq 2.8 \cdot 10^{+50}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4e-28) (not (<= z 2.8e+50)))
   (+ x (* z (+ y (* a b))))
   (+ x (+ (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4e-28) || !(z <= 2.8e+50)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + ((y * z) + (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 <= (-2.4d-28)) .or. (.not. (z <= 2.8d+50))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = x + ((y * z) + (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 <= -2.4e-28) || !(z <= 2.8e+50)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = x + ((y * z) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.4e-28) or not (z <= 2.8e+50):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = x + ((y * z) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.4e-28) || !(z <= 2.8e+50))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(x + Float64(Float64(y * z) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.4e-28) || ~((z <= 2.8e+50)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = x + ((y * z) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.4e-28], N[Not[LessEqual[z, 2.8e+50]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000002e-28 or 2.7999999999999998e50 < z

   1. Initial program 82.1%

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

      1. associate-+l+ 82.1%

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

      2. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. +-commutative 77.1%

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

      3. associate-*r* 82.5%

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

      4. distribute-rgt-in 88.3%

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

   7. Simplified 88.3%

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

   if -2.4000000000000002e-28 < z < 2.7999999999999998e50

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 90.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-28} \lor \neg \left(z \leq 2.8 \cdot 10^{+50}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+38} \lor \neg \left(z \leq 9.5 \cdot 10^{+74}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.4e+38) (not (<= z 9.5e+74)))
   (* z (+ y (* a b)))
   (+ x (+ (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.4e+38) || !(z <= 9.5e+74)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + ((y * z) + (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 <= (-5.4d+38)) .or. (.not. (z <= 9.5d+74))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + ((y * z) + (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 <= -5.4e+38) || !(z <= 9.5e+74)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + ((y * z) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.4e+38) or not (z <= 9.5e+74):
		tmp = z * (y + (a * b))
	else:
		tmp = x + ((y * z) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.4e+38) || !(z <= 9.5e+74))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(Float64(y * z) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.4e+38) || ~((z <= 9.5e+74)))
		tmp = z * (y + (a * b));
	else
		tmp = x + ((y * z) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.4e+38], N[Not[LessEqual[z, 9.5e+74]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.39999999999999992e38 or 9.5000000000000006e74 < z

   1. Initial program 77.9%

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

      1. associate-+l+ 77.9%

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

      2. associate-*l* 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in z around inf 81.1%

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

   if -5.39999999999999992e38 < z < 9.5000000000000006e74

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 88.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+38} \lor \neg \left(z \leq 9.5 \cdot 10^{+74}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-48} \lor \neg \left(z \leq 1.6 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e-48) (not (<= z 1.6e+14)))
   (* 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 <= -4.8e-48) || !(z <= 1.6e+14)) {
		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 <= (-4.8d-48)) .or. (.not. (z <= 1.6d+14))) 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 <= -4.8e-48) || !(z <= 1.6e+14)) {
		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 <= -4.8e-48) or not (z <= 1.6e+14):
		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 <= -4.8e-48) || !(z <= 1.6e+14))
		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 <= -4.8e-48) || ~((z <= 1.6e+14)))
		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, -4.8e-48], N[Not[LessEqual[z, 1.6e+14]], $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 < -4.8e-48 or 1.6e14 < z

   1. Initial program 84.0%

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

      1. associate-+l+ 84.0%

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

      2. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in z around inf 74.4%

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

   if -4.8e-48 < z < 1.6e14

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 79.3%

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

      1. +-commutative 79.3%

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

   7. Simplified 79.3%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-48} \lor \neg \left(z \leq 1.6 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-18} \lor \neg \left(a \leq 4.6 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.5e-18) (not (<= a 4.6e+107)))
   (* 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 <= -6.5e-18) || !(a <= 4.6e+107)) {
		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 <= (-6.5d-18)) .or. (.not. (a <= 4.6d+107))) 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 <= -6.5e-18) || !(a <= 4.6e+107)) {
		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 <= -6.5e-18) or not (a <= 4.6e+107):
		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 <= -6.5e-18) || !(a <= 4.6e+107))
		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 <= -6.5e-18) || ~((a <= 4.6e+107)))
		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, -6.5e-18], N[Not[LessEqual[a, 4.6e+107]], $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 < -6.50000000000000008e-18 or 4.6000000000000001e107 < a

   1. Initial program 83.5%

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

      1. associate-+l+ 83.5%

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

      2. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in a around inf 80.7%

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

   if -6.50000000000000008e-18 < a < 4.6000000000000001e107

   1. Initial program 97.9%

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

      1. associate-+l+ 97.9%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in a around 0 71.3%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-18} \lor \neg \left(a \leq 4.6 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+30} \lor \neg \left(t \leq 6 \cdot 10^{+164}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4e+30) (not (<= t 6e+164))) (* t a) (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4e+30) || !(t <= 6e+164)) {
		tmp = t * a;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4d+30)) .or. (.not. (t <= 6d+164))) then
        tmp = t * a
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4e+30) || !(t <= 6e+164)) {
		tmp = t * a;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4e+30) or not (t <= 6e+164):
		tmp = t * a
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4e+30) || !(t <= 6e+164))
		tmp = Float64(t * a);
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4e+30) || ~((t <= 6e+164)))
		tmp = t * a;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4e+30], N[Not[LessEqual[t, 6e+164]], $MachinePrecision]], N[(t * a), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0000000000000001e30 or 6.00000000000000001e164 < t

   1. Initial program 88.5%

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

      1. associate-+l+ 88.5%

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

      2. associate-*l* 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in t around inf 62.9%

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

   if -4.0000000000000001e30 < t < 6.00000000000000001e164

   1. Initial program 93.1%

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

      1. associate-+l+ 93.1%

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

      2. associate-*l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around 0 62.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+30} \lor \neg \left(t \leq 6 \cdot 10^{+164}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+30} \lor \neg \left(t \leq 2.62 \cdot 10^{+36}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.1e+30) (not (<= t 2.62e+36))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.1e+30) || !(t <= 2.62e+36)) {
		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 ((t <= (-1.1d+30)) .or. (.not. (t <= 2.62d+36))) 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 ((t <= -1.1e+30) || !(t <= 2.62e+36)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.1e+30) or not (t <= 2.62e+36):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.1e+30) || !(t <= 2.62e+36))
		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 ((t <= -1.1e+30) || ~((t <= 2.62e+36)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.1e+30], N[Not[LessEqual[t, 2.62e+36]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e30 or 2.6200000000000001e36 < t

   1. Initial program 91.1%

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

      1. associate-+l+ 91.1%

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

      2. associate-*l* 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 t around inf 57.2%

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

   if -1.1e30 < t < 2.6200000000000001e36

   1. Initial program 91.8%

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

      1. associate-+l+ 91.8%

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

      2. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around inf 37.5%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+30} \lor \neg \left(t \leq 2.62 \cdot 10^{+36}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 25.8% 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 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* 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 x around inf 24.8%

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

Developer Target 1: 97.0% 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 2024123 
(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)))