Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.6% → 96.5%

Time: 7.6s

Alternatives: 11

Speedup: 0.5×

• 31.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(b * Float64(z * a)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * fma(b, z, t));
	end
	return 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[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(b * z + t), $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 96.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 84.2

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

   5. Applied rewrites 84.2%

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

4. Final simplification 95.7%

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

Alternative 2: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+229}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.7e-45)
   (fma z y x)
   (if (<= z 2.65e-5)
     (fma a t x)
     (if (<= z 1.5e+229) (fma z y x) (* b (* z a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.7e-45) {
		tmp = fma(z, y, x);
	} else if (z <= 2.65e-5) {
		tmp = fma(a, t, x);
	} else if (z <= 1.5e+229) {
		tmp = fma(z, y, x);
	} else {
		tmp = b * (z * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.7e-45)
		tmp = fma(z, y, x);
	elseif (z <= 2.65e-5)
		tmp = fma(a, t, x);
	elseif (z <= 1.5e+229)
		tmp = fma(z, y, x);
	else
		tmp = Float64(b * Float64(z * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.7e-45], N[(z * y + x), $MachinePrecision], If[LessEqual[z, 2.65e-5], N[(a * t + x), $MachinePrecision], If[LessEqual[z, 1.5e+229], N[(z * y + x), $MachinePrecision], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.69999999999999985e-45 or 2.65e-5 < z < 1.49999999999999999e229

   1. Initial program 83.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 59.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]

   5. Applied rewrites 59.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]

   if -2.69999999999999985e-45 < z < 2.65e-5

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 77.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   5. Applied rewrites 77.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   if 1.49999999999999999e229 < z

   1. Initial program 70.9%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

   7. Applied rewrites 77.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+229}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+229}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.7e-45)
   (fma z y x)
   (if (<= z 2.65e-5)
     (fma a t x)
     (if (<= z 1.55e+229) (fma z y x) (* z (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.7e-45) {
		tmp = fma(z, y, x);
	} else if (z <= 2.65e-5) {
		tmp = fma(a, t, x);
	} else if (z <= 1.55e+229) {
		tmp = fma(z, y, x);
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.7e-45)
		tmp = fma(z, y, x);
	elseif (z <= 2.65e-5)
		tmp = fma(a, t, x);
	elseif (z <= 1.55e+229)
		tmp = fma(z, y, x);
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.7e-45], N[(z * y + x), $MachinePrecision], If[LessEqual[z, 2.65e-5], N[(a * t + x), $MachinePrecision], If[LessEqual[z, 1.55e+229], N[(z * y + x), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.69999999999999985e-45 or 2.65e-5 < z < 1.55000000000000007e229

   1. Initial program 83.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 59.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]

   5. Applied rewrites 59.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]

   if -2.69999999999999985e-45 < z < 2.65e-5

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 77.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   5. Applied rewrites 77.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   if 1.55000000000000007e229 < z

   1. Initial program 70.9%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

   7. Applied rewrites 76.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+229}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (fma a b y) x)))
   (if (<= z -3.3e-29) t_1 (if (<= z 3.5e+103) (fma a t (fma z y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, fma(a, b, y), x);
	double tmp;
	if (z <= -3.3e-29) {
		tmp = t_1;
	} else if (z <= 3.5e+103) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, fma(a, b, y), x)
	tmp = 0.0
	if (z <= -3.3e-29)
		tmp = t_1;
	elseif (z <= 3.5e+103)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b + y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -3.3e-29], t$95$1, If[LessEqual[z, 3.5e+103], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.30000000000000028e-29 or 3.5e103 < z

   1. Initial program 81.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 93.3

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

   5. Applied rewrites 93.3%

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

   if -3.30000000000000028e-29 < z < 3.5e103

   1. Initial program 96.2%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 89.8%

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

Alternative 5: 83.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(b, z, t\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+125}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (fma b z t))))
   (if (<= a -1.3e+138) t_1 (if (<= a 1.75e+125) (fma a t (fma z y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * fma(b, z, t);
	double tmp;
	if (a <= -1.3e+138) {
		tmp = t_1;
	} else if (a <= 1.75e+125) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * fma(b, z, t))
	tmp = 0.0
	if (a <= -1.3e+138)
		tmp = t_1;
	elseif (a <= 1.75e+125)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b * z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+138], t$95$1, If[LessEqual[a, 1.75e+125], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e138 or 1.75000000000000006e125 < a

   1. Initial program 71.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 90.8

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

   5. Applied rewrites 90.8%

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

   if -1.3e138 < a < 1.75000000000000006e125

   1. Initial program 96.6%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 85.9%

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

Alternative 6: 74.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \mathsf{fma}\left(a, b, y\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (fma a b y))))
   (if (<= z -3.3e-17) t_1 (if (<= z 2.45e+34) (fma a t x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * fma(a, b, y);
	double tmp;
	if (z <= -3.3e-17) {
		tmp = t_1;
	} else if (z <= 2.45e+34) {
		tmp = fma(a, t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * fma(a, b, y))
	tmp = 0.0
	if (z <= -3.3e-17)
		tmp = t_1;
	elseif (z <= 2.45e+34)
		tmp = fma(a, t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e-17], t$95$1, If[LessEqual[z, 2.45e+34], N[(a * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e-17 or 2.4500000000000001e34 < z

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 80.2

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

   5. Applied rewrites 80.2%

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

   if -3.3e-17 < z < 2.4500000000000001e34

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 76.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   5. Applied rewrites 76.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 74.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(b, z, t\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (fma b z t))))
   (if (<= a -2.5e-33) t_1 (if (<= a 2.1e-23) (fma z y x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * fma(b, z, t);
	double tmp;
	if (a <= -2.5e-33) {
		tmp = t_1;
	} else if (a <= 2.1e-23) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * fma(b, z, t))
	tmp = 0.0
	if (a <= -2.5e-33)
		tmp = t_1;
	elseif (a <= 2.1e-23)
		tmp = fma(z, y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b * z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e-33], t$95$1, If[LessEqual[a, 2.1e-23], N[(z * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.50000000000000014e-33 or 2.1000000000000001e-23 < a

   1. Initial program 82.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 74.6

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

   5. Applied rewrites 74.6%

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

   if -2.50000000000000014e-33 < a < 2.1000000000000001e-23

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 81.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]

   5. Applied rewrites 81.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 64.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.3e+75) (fma a t x) (if (<= t 3.2e+88) (fma z y x) (fma a t x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.3e+75) {
		tmp = fma(a, t, x);
	} else if (t <= 3.2e+88) {
		tmp = fma(z, y, x);
	} else {
		tmp = fma(a, t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.3e+75)
		tmp = fma(a, t, x);
	elseif (t <= 3.2e+88)
		tmp = fma(z, y, x);
	else
		tmp = fma(a, t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.3e+75], N[(a * t + x), $MachinePrecision], If[LessEqual[t, 3.2e+88], N[(z * y + x), $MachinePrecision], N[(a * t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2999999999999999e75 or 3.1999999999999999e88 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 73.3

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   5. Applied rewrites 73.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   if -2.2999999999999999e75 < t < 3.1999999999999999e88

   1. Initial program 89.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 64.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]

   5. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 59.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+25}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.9e+25) (* y z) (if (<= z 7e+104) (fma a t x) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+25) {
		tmp = y * z;
	} else if (z <= 7e+104) {
		tmp = fma(a, t, x);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.9e+25)
		tmp = Float64(y * z);
	elseif (z <= 7e+104)
		tmp = fma(a, t, x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.9e+25], N[(y * z), $MachinePrecision], If[LessEqual[z, 7e+104], N[(a * t + x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8999999999999999e25 or 7.0000000000000003e104 < z

   1. Initial program 79.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 49.4

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

   5. Applied rewrites 49.4%

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

   if -2.8999999999999999e25 < z < 7.0000000000000003e104

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 71.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   5. Applied rewrites 71.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+25}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+62}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.35e+62) (* t a) (if (<= t 1.5e+44) (* y z) (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e+62) {
		tmp = t * a;
	} else if (t <= 1.5e+44) {
		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 (t <= (-1.35d+62)) then
        tmp = t * a
    else if (t <= 1.5d+44) 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 (t <= -1.35e+62) {
		tmp = t * a;
	} else if (t <= 1.5e+44) {
		tmp = y * z;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.35e+62:
		tmp = t * a
	elif t <= 1.5e+44:
		tmp = y * z
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.35e+62)
		tmp = Float64(t * a);
	elseif (t <= 1.5e+44)
		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 (t <= -1.35e+62)
		tmp = t * a;
	elseif (t <= 1.5e+44)
		tmp = y * z;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.35e+62], N[(t * a), $MachinePrecision], If[LessEqual[t, 1.5e+44], N[(y * z), $MachinePrecision], N[(t * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e62 or 1.49999999999999993e44 < t

   1. Initial program 88.6%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 51.3

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

   5. Applied rewrites 51.3%

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

   if -1.35e62 < t < 1.49999999999999993e44

   1. Initial program 90.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 38.2

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

   5. Applied rewrites 38.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+62}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ t \cdot a \end{array} \]

FPCore

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

C

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

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 = t * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.4%

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

3. Taylor expanded in t around inf

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

   1. lower-*.f64 27.1

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

5. Applied rewrites 27.1%

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

6. Final simplification 27.1%

   \[\leadsto t \cdot a \]
7. Add Preprocessing

Developer Target 1: 97.4% accurate, 0.8× 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 2024233 
(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)))